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Popular Functions >

extreme f(x)=-x^4+x^3+2x^2

Solution

extreme points

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

Solution

Maximum (\frac{3 - 73}{8}, \frac{827 - 73 73}{512}), Minimum (0, 0), Maximum (\frac{3 + 73}{8}, \frac{827 + 73 73}{512})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < \frac{3 - 73}{8},

Decreasing

: \frac{3 - 73}{8} < x < 0,

Increasing

: 0 < x < \frac{3 + 73}{8},

Decreasing

: \frac{3 + 73}{8} < x < \infty

Plug

x = \frac{3 - 73}{8}

into

- x^{4} + x^{3} + 2 x^{2} : \frac{827 - 73 73}{512}

Maximum (\frac{3 - 73}{8}, \frac{827 - 73 73}{512})

Plug

x = 0

into

- x^{4} + x^{3} + 2 x^{2} : 0

Minimum (0, 0)

Plug

x = \frac{3 + 73}{8}

into

- x^{4} + x^{3} + 2 x^{2} : \frac{827 + 73 73}{512}

Maximum (\frac{3 + 73}{8}, \frac{827 + 73 73}{512})

Maximum (\frac{3 - 73}{8}, \frac{827 - 73 73}{512}), Minimum (0, 0), Maximum (\frac{3 + 73}{8}, \frac{827 + 73 73}{512})

Graph

Popular Examples

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in v erse f (x) = \frac{x + 1}{2 x + 3}

domain of f(x)= 1/x-4

d o main f (x) = \frac{1}{x} - 4

range of x^2+4x+4

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distance (3,-6),(-3,2)

d i s t an ce (3, - 6), (- 3, 2)

domain of f(x)=8x^2-14x+2

d o main f (x) = 8 x^{2} - 14 x + 2

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