Question

How do you find the slope of the tangent line to the graph of the given function `y=x^2`; at (2,3)?

Answer 1

here,
let f(x) =y = `x^2`

f'(x) will give you the slope of tangent

So ,
f'(x) = `dx^2/dy`
=2x
So 2x is the slope of the tangent.

TO find the slope of tangent at the point where x=2,

we have,

Slope(m) = 2*2 = 4

So the equation of tangent with slope 4 and passing through (2,3) is given by;
(y-y1)=m(x-x1)
(y-3) =4(x-2)
y-3 = 4x - 8
So,
y= 4x-5 is the equation of the tangent of the curve y= `x^2` at the point (2,3)