What is the extreme f(x)=(16x^2+25)/x ?

The extreme f(x)=(16x^2+25)/x is Maximum(-5/4 ,-40),Minimum(5/4 ,40)

Popular >

extreme f(x)=(16x^2+25)/x

extreme points

f (x) = \frac{16 x ^{2} + 25}{x}

Maximum (- \frac{5}{4}, - 40), Minimum (\frac{5}{4}, 40)

Solution steps

f^{'} (x) = \frac{16 x ^{2} - 25}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{5}{4},

Decreasing

: - \frac{5}{4} < x < 0,

Decreasing

: 0 < x < \frac{5}{4},

Increasing

: \frac{5}{4} < x < \infty

Plug

x = - \frac{5}{4}

into

\frac{16 x ^{2} + 25}{x} : - 40

Maximum (- \frac{5}{4}, - 40)

Plug

x = \frac{5}{4}

into

\frac{16 x ^{2} + 25}{x} : 40

Minimum (\frac{5}{4}, 40)

Maximum (- \frac{5}{4}, - 40), Minimum (\frac{5}{4}, 40)

y = 9 - x

f (x, y) = 2 x^{2} + 2 x y + 3 y^{2} - 16 x - 18 y + 54

+ x^{3} + 4

y = \frac{32 x}{x ^{2} + 16}

y = 2 x - 7 ln (x)

What is the extreme f(x)=(16x^2+25)/x ?
The extreme f(x)=(16x^2+25)/x is Maximum(-5/4 ,-40),Minimum(5/4 ,40)