What is the extreme y=21x+9x^2-x^3 ?

The extreme y=21x+9x^2-x^3 is Minimum(-1,-11),Maximum(7,245)

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extreme y=21x+9x^2-x^3

extreme points

y = 21 x + 9 x^{2} - x^{3}

Minimum (- 1, - 11), Maximum (7, 245)

Solution steps

f^{'} (x) = 21 + 18 x - 3 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = - 1

into

21 x + 9 x^{2} - x^{3} : - 11

Minimum (- 1, - 11)

Plug

x = 7

into

21 x + 9 x^{2} - x^{3} : 245

Maximum (7, 245)

Minimum (- 1, - 11), Maximum (7, 245)

sin (x) cos (x)

f (x) = 2 x^{2} - 8 x + y^{2} - 8 y + 6

f (x) = x^{\frac{1}{5}} (x + 24)

f (x) = \frac{x ^{3}}{3} - x^{2} - 8 x + 3

\frac{6 ∣ x ∣}{∣ x - 1 ∣}

What is the extreme y=21x+9x^2-x^3 ?
The extreme y=21x+9x^2-x^3 is Minimum(-1,-11),Maximum(7,245)