What is the extreme f(x)=-5/3 x^3+15x^2+35x+10 ?

The extreme f(x)=-5/3 x^3+15x^2+35x+10 is Minimum(-1,-25/3),Maximum(7, 1255/3)

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extreme f(x)=-5/3 x^3+15x^2+35x+10

extreme

Minimum (- 1, - \frac{25}{3}), Maximum (7, \frac{1255}{3})

Solution steps

f^{'} (x) = - 5 x^{2} + 30 x + 35

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = - 1

into

- \frac{5}{3} x^{3} + 15 x^{2} + 35 x + 10 : - \frac{25}{3}

Minimum (- 1, - \frac{25}{3})

Plug

x = 7

into

- \frac{5}{3} x^{3} + 15 x^{2} + 35 x + 10 : \frac{1255}{3}

Maximum (7, \frac{1255}{3})

Minimum (- 1, - \frac{25}{3}), Maximum (7, \frac{1255}{3})

What is the extreme f(x)=-5/3 x^3+15x^2+35x+10 ?
The extreme f(x)=-5/3 x^3+15x^2+35x+10 is Minimum(-1,-25/3),Maximum(7, 1255/3)