menu
bartleby
search
close search
Hit Return to see all results

Let f(x) = 2/3x3 + x2 − 12x + 6. Find the values of x for which the following are satisfied. (Enter your answers as comma-separated lists.)f'(x)=12f'(x)=0f'(x)=-12

Question

Let 

f(x) = 2/3x3 + x2 − 12x + 6.

 Find the values of x for which the following are satisfied. (Enter your answers as comma-separated lists.)

f'(x)=12

f'(x)=0

f'(x)=-12

check_circleAnswer
Step 1

Consider the given function.

2
+x2-12x6
3
f(x)
help_outline

Image Transcriptionclose

2 +x2-12x6 3 f(x)

fullscreen
Step 2

On differentiating with respect to x, we get

d 2
+x2 -12x6
.x5
s'(x)=
dx 3
S(x)=(3)
Bx*)+2x -12+0
f'(x)2x2 2x-12
help_outline

Image Transcriptionclose

d 2 +x2 -12x6 .x5 s'(x)= dx 3 S(x)=(3) Bx*)+2x -12+0 f'(x)2x2 2x-12

fullscreen
Step 3

If f’(x) =...

f'(x) 2x22x -12 = 12
2x22x24 = 0
xx-12 0
x24x 3x -12 0
x(x+4)-3(x+4)0
(x-3)(x+4) 0
or x+4 = 0
x-3 0
x = 3 or x = -4
help_outline

Image Transcriptionclose

f'(x) 2x22x -12 = 12 2x22x24 = 0 xx-12 0 x24x 3x -12 0 x(x+4)-3(x+4)0 (x-3)(x+4) 0 or x+4 = 0 x-3 0 x = 3 or x = -4

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Calculus

Derivative

Sorry about that. What wasn’t helpful?