What is the extreme (0.5x^2+4x-10)/(x-6) ?

The extreme (0.5x^2+4x-10)/(x-6) is Maximum(-2,2),Minimum(14,18)

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extreme (0.5x^2+4x-10)/(x-6)

extreme points

\frac{0.5 x ^{2} + 4 x - 10}{x - 6}

Maximum (- 2, 2), Minimum (14, 18)

Solution steps

f^{'} (x) = \frac{0.5 x ^{2} - 6 x - 14}{( x - 6 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 6,

Decreasing

: 6 < x < 14,

Increasing

: 14 < x < \infty

Plug

x = - 2

into

\frac{0.5 x ^{2} + 4 x - 10}{x - 6} : 2

Maximum (- 2, 2)

Plug

x = 14

into

\frac{0.5 x ^{2} + 4 x - 10}{x - 6} : 18

Minimum (14, 18)

Maximum (- 2, 2), Minimum (14, 18)

f (x) = 2 x^{2} - 8 x - 7

f (x) = 3 cos (x) + 3 sin (x)

f (x) = \frac{x ^{2} + 4}{2 x}

f (x) = (5 - x) e^{x}

f (x, y) = y^{3} - y x^{2} - 3 y^{2} \cdot x^{2} + 3 x^{4}

What is the extreme (0.5x^2+4x-10)/(x-6) ?
The extreme (0.5x^2+4x-10)/(x-6) is Maximum(-2,2),Minimum(14,18)