Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 ? 9x2 ? 108x + 2, [?3, 4]

1 answer:

4 0

Assuming the question marks are minus signs
to find max, take derivitive and test 0's and endpoints

take derivitive
f'(x)=18x²-18x-108
it equal 0 at x=-2 and 3
if we make a sign chart to find the change of signs
the sign changes from (+) to (-) at x=-2 and from (-) to (+) at x=3
so a reletive max at x=-2 and a reletive min at x=3

test entpoints

f(-3)=83
f(-2)=134
f(3)=-241
f(4)=-190

the min is at x=3 and max is at x=-2

You might be interested in

Y=-1\2+1 with a slope intercept that contains (5,6)

Semenov [28]

Answer:

y - 1/2x + 7/2

Step-by-step explanation:

y = 1/2x + 1

6 = 1/2 (5) + b

6 = 5/2 + b

7/2 = b

8 0

3 years ago

1000 times 100 in exponent

vampirchik [111]

Answer: 2^5 · 5^5

Hope it helps

7 0

3 years ago

Find the unknown side length x.

Ganezh [65]

Answer:

x = $\sqrt{65}$

Step-by-step explanation:

The altitude of the triangle must equal 4 because it is a right triangle with another leg of 3 and a hypotenuse of 5 (reason is due to the pythagorean theorem)

Therefore, the triangle on the right has legs of 4 and 7 and, again, use the phythagorean theorem to find 'x' (the hypotenuse)

$4^{2}$ + $7^{2}$ = $x^{2}$