Slope of a Curve at a Point

Key Questions

• How do I find the slope of a curve at a point?

  The slope of a curve of `y=f(x)` at `x=a` is `f'(a)`.

  Let us find the slope of `f(x)=x^3-x+2` at `x=1`.

  By taking the derivative,
  `f'(x)=3x^2-1`

  By plugging in `x=1`,
  `f'(1)=3(1)^2-1=2`

  Hence, the slope is `2`.

  Wataru · · Aug 30 2014
• Slope of a curve `y=x^2-3` at the point where `x=1`?

  First you need to find `f'(x)`, which is the derivative of `f(x)`.

  `f'(x)=2x-0=2x`

  Second, substitute in the value of x, in this case `x=1`.

  `f'(1)=2(1)=2`

  The slope of the curve `y=x^2-3` at the `x` value of `1` is `2`.

  AJ Speller · · Sep 21 2014
• What is the slope of a curve?

  Answer:

  See below

  Explanation:

  In every courve's point , the slope of a courve is defined by the tangent line in that point. See picture

  F. Javier B. · 1 · Apr 9 2018

• How do I find the slope of a curve at a point?
• How do you find the slope of a curve at a point?
• Slope of a curve `y=x^2-3` at the point where `x=1`?
• How do you use the derivative to find the slope of a curve at a point?
• How do you find the slope of a demand curve?
• What is the slope of the tangent line at a minimum of a smooth curve?
• How do you find the Slope of the curve `y=sqrt(x)` at the point where `x=4`?
• How do you find the slope of the tangent line using the formal definition of a limit?
• How do you find the slope of the tangent line to the graph of `f(x)=-x^2+4sqrt(x)` at x = 4?
• What is the slope of the line tangent to the graph of the function `f(x)=ln(sin^2(x+3))` at the point where `x=pi/3`?
• How do you find the slope of the tangent to the curve `y^3x+y^2x^2=6` at `(2,1)`?
• Find all points on the curve `x^2y^2+xy=2` where the slope of the tangent line is `-1`?
• What is the slope of `x^2y^2=9` at `(-1, 3)`?
• What is the first derivative of `x+ tanx` and how do you find the slope of the normal to the curve where `x=pi`?
• What is the slope of the line tangent to the graph of `x^2xy+y^2=7`?
• What is the slope of the line tangent to the graph of `y=e^-x`?
• What is the slope of the tangent line to the graph of `y=e^-x/x+1` at x=1?
• For the curve `y=x-x^2`, how do you find the slope of the tangent line to the curve at (1,0)?
• How do you find the slope of the tangent line for `f(x)=1/absx` at x=4?
• How do you find the slope of a tangent line to the curve `y = x - x^5` at the point (1, 0)?
• How do you find the slope of a tangent line to the graph of the function at a given point `f(x) = 3-2x` at ( -1, 5)?
• How do you find the slope of the tangent line to the graph of the equation at the point with x-coordinate for `y = sqrt(x)` at p(4,2)?
• How do you find the slope of the tangent line to the parabola `y=7x-x^2` at the point (1,6)?
• How do you find the slope of the tangent line to the graph of the function `g(x) = 4 − 8x^2` at the point (7, -388)? can somebody explain what i need to do please? and my math book isnt explaining it well by the way.?
• Consider the circle of radius 5 centered at (0,0), how do you find an equation of the line tangent to the circle at the point (3,4)?
• How do you find the tangent line slope of `f(x)=x^3-2x-3` at x=-1?
• How do you find the slope of the tangent line for `f(x) = 3x^2` at (1,3)?
• How do you find the slope of the tangent line of `f(x) = 3-2x^3` at (-1, 5)?
• What is the slope of the line tangent to the graph of `y = arctan(3x)` at x = 1?
• How do you find the slope of the tangent line to the graph of `f(x)=x^2/(x+1)` at (2, 4/3)?
• How do you find the slope of the tangent line to the curve `y=x-x^2` at (1,0)?
• How do you find the slope of the tangent to the curve `y = 3 + 4x^2 - 2x^3` where x = a?
• How do you find the slope of the tangent line to the parabola `y = x^2 + 3x` at the point (-3, 0)?
• What is the slope of a line tangent to the curve `y=t^2-6t` through the point t=4?
• How do you find the slope of the tangent to the curve `y = 1/sqrtx` at the point where x = a?
• At what points on the graph of `f(x)=2x^3-9x^2-12x+5` is the slope of the tangent line 12?
• How do you find the slope of the secant lines of `f(x)=x^3-12x+1` through the points: -3 and 3?
• How do you find the slope of the secant lines of `f(x) = -x^2` through the points: [-2, -4]?
• How do you find the slope of the secant lines of `f(x) = 2/x + 2` through the points: (0, f(0)) and (0+h, f(0+h))?
• How do you find the slope of the secant lines of `f(x) =sqrtx` through the points: [3, 5]?
• How do you find the slope of the secant lines of `f(x) = -3x + 2` through the points: (-4,(f(-4)) and (1,f(1))?
• How do you find the slope of the secant lines of `f(x) = (1/x)` through the points: (-4,(f(-4)) and (1,f(1))?
• How do you find the slope of the secant lines of `f(x)=x^2-5x` through the points: (1, f(1)) and (8, f(8) )?
• How do you find the slope of the secant lines of `f (x) = 2x^2 - 3x - 5` through the points: (2, f (2)) and (2 + h, f (2 + h)?
• How do you find the slope of the secant lines of `f(x)=6x-1x^2` through the points: `(2, f (2))` and `(2 + h, f (2 + h))`?
• How do you find the slope of the secant lines of `y=sqrt(x)` through the points: x=1 and x=4?
• How do you find the slope of the secant lines of `f(x)=6.1x^2-9.1x` through the points: x=8 and x=16?
• How do you find the slope of the secant lines of `f(x) = x^3+x` through the points: (1,f(1)) and (2,f(2))?
• How do you find the slope of the secant lines of `f(x) = sqrtx` at x=1?
• How do you find the slope of the secant lines of `f(x) = sqrtx` at P(4,2)?
• How do you find the slope of the secant lines of `y=2x^2+sec(x)` at `x=0` and `x= pi?`
• How do you find the slope of the secant lines of `f (x) = x ^2 - 4x + 5` at (1, 2) and (5, 10)?
• How do you find the slope of the secant lines of `f(x)=(x^2)-4x` at [0,4]?
• How do you find the slope of the secant lines of `f(x) = 7x^2` at `(4, f(4))` and `(4+h, f(4+h))`?
• How do you find the slope of the secant lines of `f(x) = x^2 + 5x` at (6 , f(6)) and (6 + h , f(6 + h))?
• How do you find the slope of the secant lines of `f (x) = x^2 − x − 42` at (−5, −12), and (7, 0)?
• What is the slope of `y=4x-3` at `x=-1`?
• What is the slope of `f(x)=-x^3-3` at `x=-1`?
• What is the slope of `f(x)=-e^x+3` at `x=-1`?
• What is the slope of `f(x)=-e^x+2x` at `x=1`?
• What is the slope of `f(x)=-xe^x+2x` at `x=1`?
• What is the slope of `f(x)=-xe^x-x^2` at `x=1`?
• What is the slope of `f(x)=-xe^x/x^2` at `x=1`?
• What is the slope of `f(x)=-e^x/x^2` at `x=1`?
• What is the slope of `f(x)=-e^x/(x-2` at `x=-2`?
• What is the slope of `f(x)=-e^x` at `x=-2`?
• What is the slope of `f(x)=-e^(x-3x^3)` at `x=-2`?
• What is the slope of `f(x)=-xe^(x-3x^3)` at `x=-1`?
• What is the slope of `f(x)=-X/e^(x-x^3)` at `x=-1`?
• What is the slope of `f(x)=xe^(x-x^2)` at `x=-1`?
• What is the slope of `f(x)=(x+2)/e^(x-x^2)` at `x=-1`?
• What is the equation of the line with slope `3` which is tangent to the curve `f(x)=7x-x^2`?
• Question #51aa2
• How do you find a parabola with equation `y=ax^2+bx+c` that has slope 4 at x=1, slope -8 at x=-1 and passes through (2,15)?
• How do you find the slope of the tangent line to the graph of the function `f(x)=3-2x` at (-1,5)?
• How do you find the slope of the tangent line to the graph of the function `f(x)=3/2x+1` at (-2,-2)?
• How do you find the slope of the tangent line to the graph of the function `f(x)=x^2-4` at (1,-3)?
• How do you find the slope of the tangent line to the graph of the function `f(x)=5-x^2` at (2,1)?
• How do you find the slope of the tangent line to the graph of the function `f(t)=3t-t^2` at (0,0)?
• How do you find the slope of the tangent line to the graph of the function `h(t)=t^2+3` at (-2,7)?
• Find all points where the tangent line is horizontal: `x^2+xy+y^2=1`?
• Question #0aa4d
• How do you find the slope of the graph `f(x)=-1/2+7/5x^3` at (0,-1/2)?
• How do you find the slope of the graph `f(x)=3x^3-6` at (2,18)?
• How do you find the slope of the graph `f(x)=(2x+1)^2` at (0,1)?
• How do you find the slope of the graph `f(x)=3(5-x)^2` at (5,0)?
• How do you find the slope of the graph `f(x)=4sinx-x` at (0,0)?
• How do you find the slope of the graph `g(t)=2+3cost` at (pi,-1)?
• How do you find the slope of the tangent line `y=x^3` at x=1?
• How do you find the slope of the tangent line `y=x^3-7x^2+4x+9` at x=1?
• How do you find the slope of the tangent line `y=(x+1)(x-2)` at x=1?
• How do you find the slope of the tangent line `y=(5x^2+7)^2` at x=1?
• How do you find the slope of the curve `f(x)=sqrt(x-1)` at the point x=5?
• How do you find the slope of the curve `y^3-xy^2=4` at the point where y=2?
• Question #36e66
• Question #0caf6
• Question #4ab09
• If `dy/dx = 6/(2x - 3)^2`, and `y(3) = 5`, what is the x-intercept of `y`?
• Differentiate `y^2 = 4ax` w.r.t `x` (Where a is a constant)?