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Popular >

extreme-4x^4+5x^3-x^2

Solution

extreme points

- 4 x^{4} + 5 x^{3} - x^{2}

Solution

Maximum (0, 0), Minimum (\frac{15 - 97}{32}, \frac{4523 - 485 97}{32768}), Maximum (\frac{15 + 97}{32}, \frac{4523 + 485 97}{32768})

Solution steps

f^{'} (x) = - 16 x^{3} + 15 x^{2} - 2 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{15 - 97}{32},

Increasing

: \frac{15 - 97}{32} < x < \frac{15 + 97}{32},

Decreasing

: \frac{15 + 97}{32} < x < \infty

Plug

x = 0

into

- 4 x^{4} + 5 x^{3} - x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{15 - 97}{32}

into

- 4 x^{4} + 5 x^{3} - x^{2} : \frac{4523 - 485 97}{32768}

Minimum (\frac{15 - 97}{32}, \frac{4523 - 485 97}{32768})

Plug

x = \frac{15 + 97}{32}

into

- 4 x^{4} + 5 x^{3} - x^{2} : \frac{4523 + 485 97}{32768}

Maximum (\frac{15 + 97}{32}, \frac{4523 + 485 97}{32768})

Maximum (0, 0), Minimum (\frac{15 - 97}{32}, \frac{4523 - 485 97}{32768}), Maximum (\frac{15 + 97}{32}, \frac{4523 + 485 97}{32768})

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- lo g_{3} (x) + 4

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f (x) = 2 x - 15

slope ofintercept 3x+y=-7 slope intercept

3 x + y = - 7

monotone f(x)=(9t)/(t^2+4)monotone intervals

f (x) = \frac{9 t}{t ^{2} + 4}

range of sqrt(x-3)+2 range

x - 3 + 2

Frequently Asked Questions (FAQ)

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