What is the extreme f(x)=-5x^3+x^2+x-7 ?

The extreme f(x)=-5x^3+x^2+x-7 is Minimum(-1/5 ,-178/25),Maximum(1/3 ,-182/27)

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extreme f(x)=-5x^3+x^2+x-7

extreme points

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

Minimum (- \frac{1}{5}, - \frac{178}{25}), Maximum (\frac{1}{3}, - \frac{182}{27})

Solution steps

f^{'} (x) = - 15 x^{2} + 2 x + 1

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{5},

Increasing

: - \frac{1}{5} < x < \frac{1}{3},

Decreasing

: \frac{1}{3} < x < \infty

Plug

x = - \frac{1}{5}

into

- 5 x^{3} + x^{2} + x - 7 : - \frac{178}{25}

Minimum (- \frac{1}{5}, - \frac{178}{25})

Plug

x = \frac{1}{3}

into

- 5 x^{3} + x^{2} + x - 7 : - \frac{182}{27}

Maximum (\frac{1}{3}, - \frac{182}{27})

Minimum (- \frac{1}{5}, - \frac{178}{25}), Maximum (\frac{1}{3}, - \frac{182}{27})

f (x) = x^{\frac{4}{7}} (3 x + 11)

f (x) = - 0.2 x^{2} + 1.6 x + 98.6

6 x + 18

f (x) = 5 x^{2} - x - 2

f (x) = x^{3} - 6 x^{2} + 5 [- 3.5]

What is the extreme f(x)=-5x^3+x^2+x-7 ?
The extreme f(x)=-5x^3+x^2+x-7 is Minimum(-1/5 ,-178/25),Maximum(1/3 ,-182/27)