What is the extreme f(x)=-5x^4+15x^3-17 ?

The extreme f(x)=-5x^4+15x^3-17 is Saddle(0,-17),Maximum(9/4 , 6583/256)

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extreme f(x)=-5x^4+15x^3-17

extreme points

f (x) = - 5 x^{4} + 15 x^{3} - 17

Saddle (0, - 17), Maximum (\frac{9}{4}, \frac{6583}{256})

Solution steps

f^{'} (x) = - 20 x^{3} + 45 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

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

Decreasing

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

Plug

x = 0

into

- 5 x^{4} + 15 x^{3} - 17 : - 17

Saddle (0, - 17)

Plug

x = \frac{9}{4}

into

- 5 x^{4} + 15 x^{3} - 17 : \frac{6583}{256}

Maximum (\frac{9}{4}, \frac{6583}{256})

Saddle (0, - 17), Maximum (\frac{9}{4}, \frac{6583}{256})

f (x) = x^{3} + y^{3} + 2 x^{2} + 4 y^{2} + 6

f (x) = \frac{e ^{x}}{x - 1}

f (x) = 1296 x - 0.12 x^{3}

f (x) = ln (x^{2} + 3 x + 7)

f (x) = x^{4} - x^{2} + 1

What is the extreme f(x)=-5x^4+15x^3-17 ?
The extreme f(x)=-5x^4+15x^3-17 is Saddle(0,-17),Maximum(9/4 , 6583/256)