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]

what do you need me to answer?

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.