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

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In how many ways can the letters of the word POLICEMAN be arranged if the 'word' must begin with L and end with a vowel? & W

Vladimir79 [104]

Answer:

20160 ways

Probability = 0.0556

Step-by-step explanation:

We have 9 different letters, so the total number of words we can make is:

$Total = 9! = 362880\ words$

If we want just the words that begin with L and end with a vowel, we would have the first letter "locked", so we have 8 letters remaining, and it must end with a vowel, so the last "slot" has just 4 possible values (A, E, I or O). Then we would have 4 possible values for the last letter and 7 remaining letters in the middle of the word:

$N = 4 * 7! = 4*7*6*5*4*3*2 = 20160\ words$