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Popular >

extreme f(x)=310x^3-x^2-8x+48

Solution

extreme points

f (x) = 310 x^{3} - x^{2} - 8 x + 48

Solution

Maximum (\frac{1 - 7441}{930}, \frac{7441 7441 - 11161}{1297350} + 48), Minimum (\frac{1 + 7441}{930}, \frac{- 11161 - 7441 7441}{1297350} + 48)

Solution steps

f^{'} (x) = 930 x^{2} - 2 x - 8

Find intervals:

Increasing

: - \infty < x < \frac{- 7441 + 1}{930},

Decreasing

: \frac{- 7441 + 1}{930} < x < \frac{7441 + 1}{930},

Increasing

: \frac{7441 + 1}{930} < x < \infty

Plug

x = \frac{1 - 7441}{930}

into

310 x^{3} - x^{2} - 8 x + 48 : \frac{7441 7441 - 11161}{1297350} + 48

Maximum (\frac{1 - 7441}{930}, \frac{7441 7441 - 11161}{1297350} + 48)

Plug

x = \frac{1 + 7441}{930}

into

310 x^{3} - x^{2} - 8 x + 48 : \frac{- 11161 - 7441 7441}{1297350} + 48

Minimum (\frac{1 + 7441}{930}, \frac{- 11161 - 7441 7441}{1297350} + 48)

Maximum (\frac{1 - 7441}{930}, \frac{7441 7441 - 11161}{1297350} + 48), Minimum (\frac{1 + 7441}{930}, \frac{- 11161 - 7441 7441}{1297350} + 48)

Popular Examples

inverse of f(x)=x^2-10x inverse

f (x) = x^{2} - 10 x

critical f(x)=2x+5cos(x)critical points

f (x) = 2 x + 5 cos (x)

inverse of f(x)=3+x^3 inverse

f (x) = 3 + x^{3}

slope ofintercept y=5x-2 slope intercept

y = 5 x - 2

inverse of f(x)=x^2+7x inverse

f (x) = x^{2} + 7 x

Frequently Asked Questions (FAQ)

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