What is the extreme 10+x^3-(9x^2)/2 ?

The extreme 10+x^3-(9x^2)/2 is Maximum(0,10),Minimum(3,-7/2)

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extreme 10+x^3-(9x^2)/2

extreme points

10 + x^{3} - \frac{9 x ^{2}}{2}

Maximum (0, 10), Minimum (3, - \frac{7}{2})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

10 + x^{3} - \frac{9 x ^{2}}{2} : 10

Maximum (0, 10)

Plug

x = 3

into

10 + x^{3} - \frac{9 x ^{2}}{2} : - \frac{7}{2}

Minimum (3, - \frac{7}{2})

Maximum (0, 10), Minimum (3, - \frac{7}{2})

\frac{1}{x ^{2} - 5 x - 24}

f (x) = x^{3} + 4 x^{2} + x - 6

f (x) = (x - 3)^{2} (x + 2)

f (x) = \frac{6 ( x - 7 ) ^{2}}{x + 9}

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

What is the extreme 10+x^3-(9x^2)/2 ?
The extreme 10+x^3-(9x^2)/2 is Maximum(0,10),Minimum(3,-7/2)