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Popular >

extreme f(x)=(x^3)/3-5x^2-50x+1

Solution

extreme points

f (x) = \frac{x ^{3}}{3} - 5 x^{2} - 50 x + 1

Solution

Maximum (5 (1 - 3), \frac{125 ( 10 - 6 3 )}{3} + 5003 - 749), Minimum (5 (1 + 3), \frac{125 ( 10 + 6 3 )}{3} - 749 - 5003)

Solution steps

f^{'} (x) = x^{2} - 10 x - 50

Find intervals:

Increasing

: - \infty < x < - 53 + 5,

Decreasing

: - 53 + 5 < x < 53 + 5,

Increasing

: 53 + 5 < x < \infty

Plug

x = 5 (1 - 3)

into

\frac{x ^{3}}{3} - 5 x^{2} - 50 x + 1 : \frac{125 ( 10 - 6 3 )}{3} + 5003 - 749

Maximum (5 (1 - 3), \frac{125 ( 10 - 6 3 )}{3} + 5003 - 749)

Plug

x = 5 (1 + 3)

into

\frac{x ^{3}}{3} - 5 x^{2} - 50 x + 1 : \frac{125 ( 10 + 6 3 )}{3} - 749 - 5003

Minimum (5 (1 + 3), \frac{125 ( 10 + 6 3 )}{3} - 749 - 5003)

Maximum (5 (1 - 3), \frac{125 ( 10 - 6 3 )}{3} + 5003 - 749), Minimum (5 (1 + 3), \frac{125 ( 10 + 6 3 )}{3} - 749 - 5003)

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Frequently Asked Questions (FAQ)

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