What is the extreme f(x)=-x^3+4x^2+16x-7 ?

The extreme f(x)=-x^3+4x^2+16x-7 is Minimum(-4/3 ,-509/27),Maximum(4,57)

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extreme f(x)=-x^3+4x^2+16x-7

extreme points

f (x) = - x^{3} + 4 x^{2} + 16 x - 7

Minimum (- \frac{4}{3}, - \frac{509}{27}), Maximum (4, 57)

Solution steps

f^{'} (x) = - 3 x^{2} + 8 x + 16

Find intervals:

Decreasing

: - \infty < x < - \frac{4}{3},

Increasing

: - \frac{4}{3} < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - \frac{4}{3}

into

- x^{3} + 4 x^{2} + 16 x - 7 : - \frac{509}{27}

Minimum (- \frac{4}{3}, - \frac{509}{27})

Plug

x = 4

into

- x^{3} + 4 x^{2} + 16 x - 7 : 57

Maximum (4, 57)

Minimum (- \frac{4}{3}, - \frac{509}{27}), Maximum (4, 57)

f (x, y) = 2 x^{2} + y^{2} - y

f (x) = - 7 x^{3} + 21 x + 4

x^{3} - 2 x^{2} - 4 x + 4

f (x) = 16 x + 17 x^{\frac{16}{17}}

f (x) = x^{\frac{5}{7}}

What is the extreme f(x)=-x^3+4x^2+16x-7 ?
The extreme f(x)=-x^3+4x^2+16x-7 is Minimum(-4/3 ,-509/27),Maximum(4,57)