EXAMPLE 7 Find the critical numbers of the function. f(x) = x3/5(8 − x). SOLUTION The Product Rule gives the following. f '(x) = x3/5 Correct: Your answer is correct. + (8 − x) Correct: Your answer is correct. = Correct: Your answer is correct. + 3(8 − x) Correct: Your answer is correct. = Incorrect: Your answer is incorrect. + 3(8 − x) Correct: Your answer is correct. =

Critical points: and

Step-by-step explanation:

First, the function, which is a division of two functions, has to be derived:

, where and .

The derivatives of each function are, respectively:

All components are replaced and expressed is simplified afterwards:

Let be equalized to zero and critical numbers are found by the First Derivative Test:

The critical points are:

and

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3