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Popular >

extreme f(x)=x^4-6x^3-15x^2

Solution

extreme points

f (x) = x^{4} - 6 x^{3} - 15 x^{2}

Solution

Minimum (\frac{9 - 201}{4}, \frac{9 ( 67 201 - 983 )}{32}), Maximum (0, 0), Minimum (\frac{9 + 201}{4}, - \frac{9 ( 983 + 67 201 )}{32})

Solution steps

f^{'} (x) = 4 x^{3} - 18 x^{2} - 30 x

Find intervals:

Decreasing

: - \infty < x < \frac{9 - 201}{4},

Increasing

: \frac{9 - 201}{4} < x < 0,

Decreasing

: 0 < x < \frac{9 + 201}{4},

Increasing

: \frac{9 + 201}{4} < x < \infty

Plug

x = \frac{9 - 201}{4}

into

x^{4} - 6 x^{3} - 15 x^{2} : \frac{9 ( 67 201 - 983 )}{32}

Minimum (\frac{9 - 201}{4}, \frac{9 ( 67 201 - 983 )}{32})

Plug

x = 0

into

x^{4} - 6 x^{3} - 15 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{9 + 201}{4}

into

x^{4} - 6 x^{3} - 15 x^{2} : - \frac{9 ( 983 + 67 201 )}{32}

Minimum (\frac{9 + 201}{4}, - \frac{9 ( 983 + 67 201 )}{32})

Minimum (\frac{9 - 201}{4}, \frac{9 ( 67 201 - 983 )}{32}), Maximum (0, 0), Minimum (\frac{9 + 201}{4}, - \frac{9 ( 983 + 67 201 )}{32})

Popular Examples

domain of (2x-5)/(x(x-3))domain

\frac{2 x - 5}{x ( x - 3 )}

intercepts of f(x)=-x^3+x^2+12x intercepts

f (x) = - x^{3} + x^{2} + 12 x

monotone f(x)=x^2+3x+4 monotone intervals

f (x) = x^{2} + 3 x + 4

intercepts of 3/2 sqrt(4-x^2)intercepts

\frac{3}{2} 4 - x^{2}

domain of 1/(4-x)domain

\frac{1}{4 - x}

Frequently Asked Questions (FAQ)

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