Question

I need to find the slope of the graph at x= -1

And the answer for A, B, C, D (I really need help)

Answer 1

See below

Explanation:

The derivative function f' is the slope of the function at any given 'x'

A) f ' = 8 x^3 - 24 x^2

B ) put in x = -1 and compute 8 ( -1)^3 -24(-1)^2 = -8 - 24 = - 32 slope

C) we know the slope (-32) and the x coordinate (-1) put this value of x into the original equation to find y = 2(1^4) - 8(-1)^3 + 6 = 16

so point slope form of the line is

y - 16 = -32 (x - -1) re-arrange:

y = -32x -16

D) where slope (f ') = 0 the slope is 0 and thus the tangent line is horizontal 8x^3 - 24x^2 = 0

8x^3 = 24x^2

8x = 24

x = 3