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Popular >

extreme f(x)=250x-(pix^3)/2

Solution

extreme points

f (x) = 250 x - \frac{π x ^{3}}{2}

Solution

Minimum (- \frac{10 5}{3 π}, - \frac{5000 5}{3 3 π}), Maximum (\frac{10 5}{3 π}, \frac{5000 5}{3 3 π})

Solution steps

f^{'} (x) = 250 - \frac{3 π x ^{2}}{2}

Find intervals:

Decreasing

: - \infty < x < - \frac{10 5}{3 π},

Increasing

: - \frac{10 5}{3 π} < x < \frac{10 5}{3 π},

Decreasing

: \frac{10 5}{3 π} < x < \infty

Plug

x = - \frac{10 5}{3 π}

into

250 x - \frac{π x ^{3}}{2} : - \frac{5000 5}{3 3 π}

Minimum (- \frac{10 5}{3 π}, - \frac{5000 5}{3 3 π})

Plug

x = \frac{10 5}{3 π}

into

250 x - \frac{π x ^{3}}{2} : \frac{5000 5}{3 3 π}

Maximum (\frac{10 5}{3 π}, \frac{5000 5}{3 3 π})

Minimum (- \frac{10 5}{3 π}, - \frac{5000 5}{3 3 π}), Maximum (\frac{10 5}{3 π}, \frac{5000 5}{3 3 π})

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=250x-(pix^3)/2 ?
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