What is the extreme f(x)=-x^3+7x^2-15x ?

The extreme f(x)=-x^3+7x^2-15x is Minimum(5/3 ,-275/27),Maximum(3,-9)

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extreme f(x)=-x^3+7x^2-15x

extreme points

f (x) = - x^{3} + 7 x^{2} - 15 x

Minimum (\frac{5}{3}, - \frac{275}{27}), Maximum (3, - 9)

Solution steps

f^{'} (x) = - 3 x^{2} + 14 x - 15

Find intervals:

Decreasing

: - \infty < x < \frac{5}{3},

Increasing

: \frac{5}{3} < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = \frac{5}{3}

into

- x^{3} + 7 x^{2} - 15 x : - \frac{275}{27}

Minimum (\frac{5}{3}, - \frac{275}{27})

Plug

x = 3

into

- x^{3} + 7 x^{2} - 15 x : - 9

Maximum (3, - 9)

Minimum (\frac{5}{3}, - \frac{275}{27}), Maximum (3, - 9)

\frac{x ^{2} - 2 x + 1}{x ^{3} - 3 x ^{2}}

f (x) = \frac{2 x - 3}{7 x + 5}

y = - x + 2

(5 x^{2} + 6 x - 2) (x - 5)

f (x) = 1 + (10 + x)^{\frac{1}{2}}

What is the extreme f(x)=-x^3+7x^2-15x ?
The extreme f(x)=-x^3+7x^2-15x is Minimum(5/3 ,-275/27),Maximum(3,-9)