Question

Consider the following cubic curve:
f(x)=−x3 −x2 +16x+16

1. Calculate f′(x).
2. Calculate f′′(x).
3. Find the x values such that f(x) = 0.

Answer 1

Assuming you meant:
f(x)=?x^3 ?x^2 +16x+16

f ' (x) = -3x^2 - 2x + 16
f ''(x) = -6x - 2

If you are studying Calculus or Pre-Calculus, you MUST know how to do this.

if f(x) = 0
?x^3 ?x^2 +16x+16 = 0
x^3 + x^2 - 16x - 16 = 0
by grouping,
x^2(x+1) - 16(x+1) = 0
(x+1)(x^2 - 16) = 0
(x+1)(x-4)(x+4) = 0
x = -1, 4, -4

verification:
http://www.wolframalpha.com/input/?i=plot+f(x)%3D%E2%88%92x%5E3+%E2%88%92x%5E2+%2B16x%2B16

Answer 2

Why did you repost this question ??
Just noticed that Steve answered it for you several days ago

http://www.jiskha.com/display.cgi?id=1483135842