What is the extreme 4x^3+9x^2-54x+6 ?

The extreme 4x^3+9x^2-54x+6 is Maximum(-3,141),Minimum(3/2 ,-165/4)

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extreme 4x^3+9x^2-54x+6

extreme

Maximum (- 3, 141), Minimum (\frac{3}{2}, - \frac{165}{4})

Solution steps

f^{'} (x) = 12 x^{2} + 18 x - 54

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < \frac{3}{2},

Increasing

: \frac{3}{2} < x < \infty

Plug

x = - 3

into

4 x^{3} + 9 x^{2} - 54 x + 6 : 141

Maximum (- 3, 141)

Plug

x = \frac{3}{2}

into

4 x^{3} + 9 x^{2} - 54 x + 6 : - \frac{165}{4}

Minimum (\frac{3}{2}, - \frac{165}{4})

Maximum (- 3, 141), Minimum (\frac{3}{2}, - \frac{165}{4})

What is the extreme 4x^3+9x^2-54x+6 ?
The extreme 4x^3+9x^2-54x+6 is Maximum(-3,141),Minimum(3/2 ,-165/4)