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Popular Functions >

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

Solution

extreme

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)=x^4+x^2

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

extreme f(x)=380x^2-3800x^3

extreme f(x)=3x^4-4x^3-12x^2+1[-2.3]

extreme f(x)=8x^3-3xy+y^3

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)