Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 9x2 − 108x + 5, [−3, 4] absolute minimum value absolute maximum value

ANSWER

(-2,137) is an absolute maximum on the closed interval [-3,4]

(3,-238) is an absolute minimum on the closed interval [-3,4]

EXPLANATION

The given polynomial function is:

We find the first derivative to obtain:

At turning points,

This implies that,

The solutions to this quadratic equation is:

We substitute these x-values into the original functions to get the two turning points.

When x=-2, f(-2)=137

When x=3, f(3)=-238

The turning point are:

We use the second derivative test to determine which of them is an absolute minimum or maximum on the closed interval [-3,4]

This implies that, (-2,137) is an absolute maximum on the closed interval [-3,4]

This implies that, (3,-238) is an absolute minimum on the closed interval [-3,4]

center= (-2,0)

radius= sqrt2/2

step-by-step explanation:

the answer is (-8,-5)

step-by-step explanation:

the endpoint to midpoint is half the length. the length is (-2,-1) so when you are at the midpoint just add it to it to find your answer -6+(-2)= -8 and -4+(-1)=-5 so (-8,-5)