Find all relative extrema and classify each as a maximum or minimum. Use the second-derivative test where possible. f(x) = 125x 3 − 15x + 8

The following classification is found:

- Absolute minimum

- Absolute maximum

Step-by-step explanation:

Let be , we need to find first and second derivatives of this expression at first:

First derivative

(Eq. 1)

Second derivative

(Eq. 2)

Critical points are points that equals first derivative to zero and that may be maxima or minima. That is:

Which leads to the following critical points:

and

Now we evaluate each result in second derivative expression:

(Absolute minimum)

(Absolute maximum)

Lastly we evaluate the function at each critical point:

And the following classification is found:

- Absolute minimum

- Absolute maximum

true

step-by-step explanation:

answer: a) (0,0), (1,1), (2,8), and (3,27).

step-by-step explanation:

0^3=0

1^3=1

2^3=8

3^3=27

in effect, the exponential equation for this would me y=3^x. each x-coordinate cubed is giving the y coordinate, so a is your answer : )