What is the extreme ((x^2+16))/((x-3)) ?

The extreme ((x^2+16))/((x-3)) is Maximum(-2,-4),Minimum(8,16)

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extreme ((x^2+16))/((x-3))

extreme points

\frac{( x ^{2} + 16 )}{( x - 3 )}

Maximum (- 2, - 4), Minimum (8, 16)

Solution steps

f^{'} (x) = \frac{x ^{2} - 6 x - 16}{( x - 3 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 3,

Decreasing

: 3 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = - 2

into

\frac{x ^{2} + 16}{x - 3} : - 4

Maximum (- 2, - 4)

Plug

x = 8

into

\frac{x ^{2} + 16}{x - 3} : 16

Minimum (8, 16)

Maximum (- 2, - 4), Minimum (8, 16)

540 x - 5 x^{3}

f (x) = 232 x - 5000 - x^{2}

f (x) = 5 x^{\frac{4}{5}} - x, 0 \leq x \leq 3025

\frac{e ^{2 x}}{x}

What is the extreme ((x^2+16))/((x-3)) ?
The extreme ((x^2+16))/((x-3)) is Maximum(-2,-4),Minimum(8,16)