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Popular >

extreme f(x)=-12x^5+45x^4+40x^3-3

Solution

extreme points

f (x) = - 12 x^{5} + 45 x^{4} + 40 x^{3} - 3

Solution

Minimum (\frac{3 - 17}{2}, \frac{3 ( 123 - 29 17 )}{2} + 897 - 22017), Saddle (0, - 3), Maximum (\frac{3 + 17}{2}, \frac{3 ( 123 + 29 17 )}{2} + 897 + 22017)

Solution steps

f^{'} (x) = - 60 x^{4} + 180 x^{3} + 120 x^{2}

Find intervals:

Decreasing

: - \infty < x < \frac{3 - 17}{2},

Increasing

: \frac{3 - 17}{2} < x < 0,

Increasing

: 0 < x < \frac{3 + 17}{2},

Decreasing

: \frac{3 + 17}{2} < x < \infty

Plug

x = \frac{3 - 17}{2}

into

- 12 x^{5} + 45 x^{4} + 40 x^{3} - 3 : \frac{3 ( 123 - 29 17 )}{2} + 897 - 22017

Minimum (\frac{3 - 17}{2}, \frac{3 ( 123 - 29 17 )}{2} + 897 - 22017)

Plug

x = 0

into

- 12 x^{5} + 45 x^{4} + 40 x^{3} - 3 : - 3

Saddle (0, - 3)

Plug

x = \frac{3 + 17}{2}

into

- 12 x^{5} + 45 x^{4} + 40 x^{3} - 3 : \frac{3 ( 123 + 29 17 )}{2} + 897 + 22017

Maximum (\frac{3 + 17}{2}, \frac{3 ( 123 + 29 17 )}{2} + 897 + 22017)

Minimum (\frac{3 - 17}{2}, \frac{3 ( 123 - 29 17 )}{2} + 897 - 22017), Saddle (0, - 3), Maximum (\frac{3 + 17}{2}, \frac{3 ( 123 + 29 17 )}{2} + 897 + 22017)

Popular Examples

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=-12x^5+45x^4+40x^3-3 ?
The extreme f(x)=-12x^5+45x^4+40x^3-3 is