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Popular >

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

Solution

extreme points

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

Solution

Saddle (0, 0), Maximum (1, 1)

Solution steps

f^{'} (x) = 12 x^{2} - 12 x^{3}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 1

into

4 x^{3} - 3 x^{4} : 1

Maximum (1, 1)

Saddle (0, 0), Maximum (1, 1)

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=4x^3-3x^4 ?
The extreme f(x)=4x^3-3x^4 is Saddle(0,0),Maximum(1,1)