# Thread: Maximum and minimum of function in the interval

1. ## Maximum and minimum of function in the interval

Maximum and minimum of $f(x) = 3x^4 - 8x^3 -48x^2 + 5$ in the interval $-3 \leq x \leq 5$

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$f'(x) = 12x^3 - 24x^2 - 96x$

Now what do I do?

2. Originally Posted by Critter314
$f(x) = 3x^4 - 8x^3 -48x^2 + 5$

Interval

$-3 \leq x \leq 5$

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$f'(x) = 12x^3 - 24x^2 - 96x$

Now what do I do?
set f'(x) = 0 to determine critical values since extrema occur at critical values.

don't forget to check the value of f(x) at the endpoints.

3. note that $[-3,5]$ is a compact set and $f$ is continuous, thus by the Extreme Value Theorem $f$ is $f(-3)\le f(x)\le f(5).$