What is the extreme f(x)=0.25x^4+x^3 ?

The extreme f(x)=0.25x^4+x^3 is Minimum(-3,-6.75),Saddle(0,0)

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extreme f(x)=0.25x^4+x^3

extreme points

f (x) = 0.25 x^{4} + x^{3}

Minimum (- 3, - 6.75), Saddle (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

0.25 x^{4} + x^{3} : - 6.75

Minimum (- 3, - 6.75)

Plug

x = 0

into

0.25 x^{4} + x^{3} : 0

Saddle (0, 0)

Minimum (- 3, - 6.75), Saddle (0, 0)

p (a, b) = (a \cdot e) - 2200 - 0.02 \cdot e - b

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

f (x) = \frac{x}{x ^{2} - 49}

7 x (1 + 12 x^{2})^{- 2}

f (x) = 4 sin (x) + 3 cos (x), 0 \leq x \leq 2 π

What is the extreme f(x)=0.25x^4+x^3 ?
The extreme f(x)=0.25x^4+x^3 is Minimum(-3,-6.75),Saddle(0,0)