Asked Oct 20, 2019
Let f (x) = x1/3(4x + 6)2/3.   Find f ' (x) and the critical numbers for f.

f ' (x) = 
Ax + B
3 xC (4x + 6)D
, where
A =
B =
C =
D =

The critical numbers of f are (list in increasing order):
x =
x =
x =

(Enter DNE in any unused answer blank.)


Expert Answer

Step 1

Use product rule to find f'(x). 


Image Transcriptionclose

2 f(x)=x3 (4x+6) 2 2 f'(x)=(x3)(4x+6)3 x (4x+6) 3 2 2 1 2 (4x+6)x 3 f'(x)=X 3 (4x+6) 2 (4x+6) X f'(x)= 2 3 3x 3(4x+6)

Step 2

Simplify it using LCD

Answer: A=5, B=6, ...


Image Transcriptionclose

2 3 X (4x+6) f'(x)= 2 Зx 3(4x+6) 2 (4х+6) ' (4х+6)* +x *x 3 f'(x)= 2 Зх 3 (4x+6) 4x+6+х г')- 2 Зх (4х+6) 3 5х+6 f'(x) 2 Зх 3 (4х+6) - |.


Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in




Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A

Q: Jane is ?=2 mi offshore in a boat and wishes to reach a coastal village ?=7 mi down a straight shore...

A: Consider the given information:


Q: Find the number of units x that produces the minimum average cost per unit  C  in the given equation...

A: Given that


Q: $280 for a party of 5, cost per plate is $15, write an equation that models the cost of a dinner.

A: The cost per plate is given as $15 and the total production cost is $280 for the party of 5.The cost...


Q: A (square) baseball diamond has sides that are 90 feet long. A player 21 feet from third base is run...

A: The scenario given in the above question can be pictorially depicted as


Q: Two people start biking from the same point. One heads east at 13 mph, the other south at 17 mph. Wh...

A: Given, two bikers start at same point. One heading east at 13mph and other heading south at 17 mph.


Q: Calculus Question

A: Given that, P / T = k.This implies that, P = kT.Differentiate the function with respect to t.


Q: r4 2V dx Vx 15. 1

A: The integral is given by,


Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and secon...

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test is:f''(x...


Q: As a fungus​ grows, its rate of growth changes. Young fungi grow​ exponentially, while in larger fun...

A: The function R(t) represents the model of rate of growth of fungus as a function of time.