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Popular >

extreme f(x)=3x+4sqrt(32.5-x^2)

Solution

extreme points

f (x) = 3 x + 4 32.5 - x^{2}

Solution

Minimum (- \frac{65}{2}, - 17.10263 \dots), Maximum (\frac{3 13}{10}, 28.50438 \dots), Minimum (\frac{65}{2}, 17.10263 \dots)

Solution steps

f^{'} (x) = 3 - \frac{4 x}{32.5 - x ^{2}}

Find intervals:

Increasing

: - \frac{65}{2} < x < \frac{3 13}{10},

Decreasing

: \frac{3 13}{10} < x < \frac{65}{2}

Plug

x = - \frac{65}{2}

into

3 x + 4 32.5 - x^{2} : - 17.10263 \dots

Minimum (- \frac{65}{2}, - 17.10263 \dots)

Plug

x = \frac{3 13}{10}

into

3 x + 4 32.5 - x^{2} : 28.50438 \dots

Maximum (\frac{3 13}{10}, 28.50438 \dots)

Plug

x = \frac{65}{2}

into

3 x + 4 32.5 - x^{2} : 17.10263 \dots

Minimum (\frac{65}{2}, 17.10263 \dots)

Minimum (- \frac{65}{2}, - 17.10263 \dots), Maximum (\frac{3 13}{10}, 28.50438 \dots), Minimum (\frac{65}{2}, 17.10263 \dots)

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Frequently Asked Questions (FAQ)

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