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Popular Functions >

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

Solution

extreme

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)

Graph

Popular Examples

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extreme f(x)=4x^3-12x^2-96x+7

extreme f(x,y)=sqrt(-25x^2+250x-y^2+8y-637)

Frequently Asked Questions (FAQ)

What is the extreme f(x)=3x+4sqrt(32.5-x^2) ?
The extreme f(x)=3x+4sqrt(32.5-x^2) is