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

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

answer: the anser is 3

step-by-step explanation:

c- 2o is equal to 9