Question

(a) Find the slope of the curve y+x^3 -8x at the given point P(2,-8) by finding the limiting value of the slope of the secants through P.

(b) find an equation of the tangent line to the curve at P(2,-8)


(a) the slope of the curve at P(2,-8) is |?|

Answer 1

(a) Slope is 4

(b) Equation of tangent line is y=4x-16

Explanation:

Find the derivative and substitute x=2

`y=x^3-8x\\y'=3x^2-8\\y'=3(2)^2-8\\y'=3(4)-8\\y'=12-8\\y'=4`

Use point-slope form to get the tangent line equation

`y-y_1=m(x-x_1)\\y-(-8)=4(x-2)\\y+8=4(x-2)\\y+8=4x-8\\y=4x-16`