Find the local maximum and minimum values of f using both the First and Second Derivative Tests. f(x) = 6 + 12x2 − 8x3

The local maximum is at x = 0 and local minimum is at x = 1

Step-by-step explanation:

f(x) = 6 + 12x² - 8x³

The second derivative test is as follows:

When a function's slope is zero at x, and the second derivative at x is:

i) less than 0, it is a local maximum

ii) greater than 0, it is a local minimum

iii) equal to 0, then the test fails

The local maximum is at x = 0 and local minimum is at x = 1