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

The extreme (x^2)/(x^2+2x-15) is Maximum(0,0),Minimum(15, 15/16)

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extreme (x^2)/(x^2+2x-15)

extreme points

\frac{x ^{2}}{x ^{2} + 2 x - 15}

Maximum (0, 0), Minimum (15, \frac{15}{16})

Solution steps

f^{'} (x) = \frac{2 x ^{2} - 30 x}{( x ^{2} + 2 x - 15 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 0,

Decreasing

: 0 < x < 3,

Decreasing

: 3 < x < 15,

Increasing

: 15 < x < \infty

Plug

x = 0

into

\frac{x ^{2}}{x ^{2} + 2 x - 15} : 0

Maximum (0, 0)

Plug

x = 15

into

\frac{x ^{2}}{x ^{2} + 2 x - 15} : \frac{15}{16}

Minimum (15, \frac{15}{16})

Maximum (0, 0), Minimum (15, \frac{15}{16})

f (x, y) = - x^{2} + 5 y^{2} + 10 x - 10 y - 28

y = (x - 2)^{2} (x + 4)

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

f (x) = 120 x - 0.4 x^{4} + 1000

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

What is the extreme (x^2)/(x^2+2x-15) ?
The extreme (x^2)/(x^2+2x-15) is Maximum(0,0),Minimum(15, 15/16)