What is the extreme f(x)=-5x^4+5x^3-10 ?

The extreme f(x)=-5x^4+5x^3-10 is Saddle(0,-10),Maximum(3/4 ,-2425/256)

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extreme f(x)=-5x^4+5x^3-10

extreme points

f (x) = - 5 x^{4} + 5 x^{3} - 10

Saddle (0, - 10), Maximum (\frac{3}{4}, - \frac{2425}{256})

Solution steps

f^{'} (x) = - 20 x^{3} + 15 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{3}{4},

Decreasing

: \frac{3}{4} < x < \infty

Plug

x = 0

into

- 5 x^{4} + 5 x^{3} - 10 : - 10

Saddle (0, - 10)

Plug

x = \frac{3}{4}

into

- 5 x^{4} + 5 x^{3} - 10 : - \frac{2425}{256}

Maximum (\frac{3}{4}, - \frac{2425}{256})

Saddle (0, - 10), Maximum (\frac{3}{4}, - \frac{2425}{256})

f (x, y) = 3 x^{- 2} + 5 y^{- 2} + 8 x y^{2}

f (x, y) = 4 x^{4} + 4 y^{4} - x y

f (x) = ln (x + y)

f (x) = x + 3 x^{\frac{2}{3}}

f (x, y) = x^{3} + 3 x y + y^{3}

What is the extreme f(x)=-5x^4+5x^3-10 ?
The extreme f(x)=-5x^4+5x^3-10 is Saddle(0,-10),Maximum(3/4 ,-2425/256)