Question

What is the equation of the tangent line of `f(x)=x^(3) + 2x^(2) - 3x + 2` at `x=1`?

Answer 1

y= 4x - 2

Explanation:

To find the equation of the tangent in the form y=mx +c , where m represents the gradient and c , the y-intercept.
Require to find m and c . m can be found by evaluating f'(1) and c by evaluating f(1).

`f'(x) = 3x^2 + 4x - 3`

and f'(1) `= 3(1)^2 + 4(1) -3 = 4 = m " gradient of tangent "`

partial equation is: y = 4x +c

now f(1) `= (1)^3 + 2(1)^2 - 3(1) + 2 = 2 rArr (1,2) " is tangent point "`

substitute (1,2) into y = 4x + c to calculate value of c.

hence : 2 = 4 + c → c = -2

`"equation of tangent is " y = 4x - 2`