Question
Asked Oct 18, 2019

Determine the location and value of the absolute extreme values of f on the given interval, if they exist.

f(x)=cos3x on [-pi/4 , pi/2]

what is/are the absolute maximum/maxima of f on the given interval?

what is/are the absolute mininum/minima of f on the given interval?

check_circleExpert Solution
Step 1

Compute as follows.

...
f(x)= cos3x
f'(x)=-3sin 3x
f'(x)=0
>-3sin3x = 0
sin 3.x 0
Зх 3 0, л
-
x = 0,
3
differentiate f(x) = -3sin3x with respect to x
f"(x)=-9cos3x
Note that f"(x) <0 atx 0 that is, maximum exists at x 0
that is, minimum exists at x =
3
f"(x)>0 at x
3
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f(x)= cos3x f'(x)=-3sin 3x f'(x)=0 >-3sin3x = 0 sin 3.x 0 Зх 3 0, л - x = 0, 3 differentiate f(x) = -3sin3x with respect to x f"(x)=-9cos3x Note that f"(x) <0 atx 0 that is, maximum exists at x 0 that is, minimum exists at x = 3 f"(x)>0 at x 3

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