What is the extreme 13x^2(x-10)+15 ?

The extreme 13x^2(x-10)+15 is Maximum(0,15),Minimum(20/3 ,-51595/27)

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extreme 13x^2(x-10)+15

extreme points

13 x^{2} (x - 10) + 15

Maximum (0, 15), Minimum (\frac{20}{3}, - \frac{51595}{27})

Solution steps

f^{'} (x) = 13 x (3 x - 20)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{20}{3},

Increasing

: \frac{20}{3} < x < \infty

Plug

x = 0

into

13 x^{2} (x - 10) + 15 : 15

Maximum (0, 15)

Plug

x = \frac{20}{3}

into

13 x^{2} (x - 10) + 15 : - \frac{51595}{27}

Minimum (\frac{20}{3}, - \frac{51595}{27})

Maximum (0, 15), Minimum (\frac{20}{3}, - \frac{51595}{27})

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

x^{3} - 3 x - 6

f (x, y) = 3 x^{2} + y^{2} - 2 x y + 42 - 8 y

y = - 3 cos (x), 0 \leq x \leq 2 π

x^{2} - 2 x y + 3 y^{2} - 20 y

What is the extreme 13x^2(x-10)+15 ?
The extreme 13x^2(x-10)+15 is Maximum(0,15),Minimum(20/3 ,-51595/27)