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Popular >

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

Solution

extreme points

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

Solution

Minimum (- \frac{3}{4}, - \frac{27}{256}), Saddle (0, 0)

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Increasing

: 0 < x < \infty

Plug

x = - \frac{3}{4}

into

x^{4} + x^{3} : - \frac{27}{256}

Minimum (- \frac{3}{4}, - \frac{27}{256})

Plug

x = 0

into

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

Saddle (0, 0)

Minimum (- \frac{3}{4}, - \frac{27}{256}), Saddle (0, 0)

Graph

Popular Examples

extreme f(x)=(3x)/(x^2+16)extreme points

f (x) = \frac{3 x}{x ^{2} + 16}

extreme f(x)=x^4+x^2 extreme points

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

extreme f(x)x^3-27x extreme points

f (x) x^{3} - 27 x

extreme f(x)=3x^2-2x+4 extreme points

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

extreme f(x)=x^2-14x+9 extreme points

f (x) = x^{2} - 14 x + 9

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^4+x^3 ?
The extreme f(x)=x^4+x^3 is Minimum(-3/4 ,-27/256),Saddle(0,0)