What is the extreme-1/(x^2+49)-1/((x-5)^2+4) ?

The extreme-1/(x^2+49)-1/((x-5)^2+4) is Minimum(4.98537…,-0.26352…)

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extreme-1/(x^2+49)-1/((x-5)^2+4)

extreme points

- \frac{1}{x ^{2} + 49} - \frac{1}{( x - 5 ) ^{2} + 4}

Minimum (4.98537 \dots, - 0.26352 \dots)

Solution steps

Find the critical points:

x \approx 4.98537 \dots

Domain of

- \frac{1}{x ^{2} + 49} - \frac{1}{( x - 5 ) ^{2} + 4} : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 4.98537 \dots,

Increasing

: 4.98537 \dots < x < \infty

Plug the extreme point

x = 4.98537 \dots

into

- \frac{1}{x ^{2} + 49} - \frac{1}{( x - 5 ) ^{2} + 4} \Rightarrow y = - 0.26352 \dots

Minimum (4.98537 \dots, - 0.26352 \dots)

f (x) = x \cdot (ln (x))^{2}

f (x) = x [36 - 2 (x)]^{2}

f (x) = x + 12 - 8

f (x, y) = 4 x y + 120 y - 20 y^{2} - \frac{1}{10} x^{2} y - 90

f (x, y) = 2 x^{2} + 4 y^{2} - 2 x y - 10 x - 2 y + 2

What is the extreme-1/(x^2+49)-1/((x-5)^2+4) ?
The extreme-1/(x^2+49)-1/((x-5)^2+4) is Minimum(4.98537…,-0.26352…)