What is the extreme f(x)=14+16x-5x^2+((x^3)/3) ?

The extreme f(x)=14+16x-5x^2+((x^3)/3) is Maximum(2, 86/3),Minimum(8,-22/3)

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extreme f(x)=14+16x-5x^2+((x^3)/3)

extreme points

f (x) = 14 + 16 x - 5 x^{2} + (\frac{x ^{3}}{3})

Maximum (2, \frac{86}{3}), Minimum (8, - \frac{22}{3})

Solution steps

f^{'} (x) = x^{2} - 10 x + 16

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = 2

into

14 + 16 x - 5 x^{2} + \frac{x ^{3}}{3} : \frac{86}{3}

Maximum (2, \frac{86}{3})

Plug

x = 8

into

14 + 16 x - 5 x^{2} + \frac{x ^{3}}{3} : - \frac{22}{3}

Minimum (8, - \frac{22}{3})

Maximum (2, \frac{86}{3}), Minimum (8, - \frac{22}{3})

x^{2} + y^{2} - 6 x - 6 y + 5

f (x) = x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 8

x^{3} - 2 x^{2} - 2

f (x) = 168000 - 200 x

2 x y

What is the extreme f(x)=14+16x-5x^2+((x^3)/3) ?
The extreme f(x)=14+16x-5x^2+((x^3)/3) is Maximum(2, 86/3),Minimum(8,-22/3)