What is the extreme 3x^4+7x^3-18^2-32 ?

The extreme 3x^4+7x^3-18^2-32 is Minimum(-7/4 ,-93537/256),Saddle(0,-356)

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extreme 3x^4+7x^3-18^2-32

extreme

Minimum (- \frac{7}{4}, - \frac{93537}{256}), Saddle (0, - 356)

Solution steps

f^{'} (x) = 12 x^{3} + 21 x^{2}

Find intervals:

Decreasing

: - \infty < x < - \frac{7}{4},

Increasing

: - \frac{7}{4} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{7}{4}

into

3 x^{4} + 7 x^{3} - 1 8^{2} - 32 : - \frac{93537}{256}

Minimum (- \frac{7}{4}, - \frac{93537}{256})

Plug

x = 0

into

3 x^{4} + 7 x^{3} - 1 8^{2} - 32 : - 356

Saddle (0, - 356)

Minimum (- \frac{7}{4}, - \frac{93537}{256}), Saddle (0, - 356)

What is the extreme 3x^4+7x^3-18^2-32 ?
The extreme 3x^4+7x^3-18^2-32 is Minimum(-7/4 ,-93537/256),Saddle(0,-356)