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Popular Functions >

extreme x^4-5x^3

Solution

extreme points

x^{4} - 5 x^{3}

Solution

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

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

Increasing

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

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = \frac{15}{4}

into

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

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

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

Graph

Popular Examples

extreme f(x,y)=x^3-y^3-2xy+6

extreme f(x)=-x^2+160x-400

extreme f(x)=x^4-5x^2

Frequently Asked Questions (FAQ)

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