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

The extreme f(x)=5x^3+x^4 is Minimum(-15/4 ,-16875/256),Saddle(0,0)

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

extreme points

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

Minimum (- \frac{15}{4}, - \frac{16875}{256}), Saddle (0, 0)

Solution steps

f^{'} (x) = 15 x^{2} + 4 x^{3}

Find intervals:

Decreasing

: - \infty < x < - \frac{15}{4},

Increasing

: - \frac{15}{4} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{15}{4}

into

5 x^{3} + x^{4} : - \frac{16875}{256}

Minimum (- \frac{15}{4}, - \frac{16875}{256})

Plug

x = 0

into

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

Saddle (0, 0)

Minimum (- \frac{15}{4}, - \frac{16875}{256}), Saddle (0, 0)

f (x) = 9 x^{2} - 4 x

f (x) = - (x + 1)^{2} \cdot (x + 3)^{3} \cdot (x - 4)^{2}

f (x) = 5 e^{x} - e^{2 x}

f (x, y) = 4 x^{2} + 2 y^{2} + 5

1 - ∣ x ∣

What is the extreme f(x)=5x^3+x^4 ?
The extreme f(x)=5x^3+x^4 is Minimum(-15/4 ,-16875/256),Saddle(0,0)