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Popular >

extreme x^4+3x^3-6

Solution

extreme points

x^{4} + 3 x^{3} - 6

Solution

Minimum (- \frac{9}{4}, - \frac{3723}{256}), Saddle (0, - 6)

Solution steps

f^{'} (x) = 4 x^{3} + 9 x^{2}

Find intervals:

Decreasing

: - \infty < x < - \frac{9}{4},

Increasing

: - \frac{9}{4} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{9}{4}

into

x^{4} + 3 x^{3} - 6 : - \frac{3723}{256}

Minimum (- \frac{9}{4}, - \frac{3723}{256})

Plug

x = 0

into

x^{4} + 3 x^{3} - 6 : - 6

Saddle (0, - 6)

Minimum (- \frac{9}{4}, - \frac{3723}{256}), Saddle (0, - 6)

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Frequently Asked Questions (FAQ)

What is the extreme x^4+3x^3-6 ?
The extreme x^4+3x^3-6 is Minimum(-9/4 ,-3723/256),Saddle(0,-6)