What is the extreme (x-521)/(x^2+x-132) ?

The extreme (x-521)/(x^2+x-132) is

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extreme (x-521)/(x^2+x-132)

extreme points

\frac{x - 521}{x ^{2} + x - 132}

Minimum (521 - 271830, \frac{283518690 + 543660 271830}{295709993670 - 54366 0 ^{2}}), Maximum (521 + 271830, \frac{283518690 - 543660 271830}{295709993670 - 54366 0 ^{2}})

Solution steps

Find the critical points:

x = 521 - 271830, x = 521 + 271830

Domain of

\frac{x - 521}{x ^{2} + x - 132} : x < - 12 or - 12 < x < 11 or x > 11

Find intervals:

Decreasing

: - \infty < x < - 12,

Decreasing

: - 12 < x < 521 - 271830,

Increasing

: 521 - 271830 < x < 11,

Increasing

: 11 < x < 521 + 271830,

Decreasing

: 521 + 271830 < x < \infty

Plug the extreme point

x = 521 - 271830

into

\frac{x - 521}{x ^{2} + x - 132} \Rightarrow y = \frac{283518690 + 543660 271830}{295709993670 - 54366 0 ^{2}}

Minimum (521 - 271830, \frac{283518690 + 543660 271830}{295709993670 - 54366 0 ^{2}})

Plug the extreme point

x = 521 + 271830

into

\frac{x - 521}{x ^{2} + x - 132} \Rightarrow y = \frac{283518690 - 543660 271830}{295709993670 - 54366 0 ^{2}}

Maximum (521 + 271830, \frac{283518690 - 543660 271830}{295709993670 - 54366 0 ^{2}})

Minimum (521 - 271830, \frac{283518690 + 543660 271830}{295709993670 - 54366 0 ^{2}}), Maximum (521 + 271830, \frac{283518690 - 543660 271830}{295709993670 - 54366 0 ^{2}})

f (x) = 8 x^{3} - 7 ln (x^{3}), (0.12, 7)

3 x^{4} - 2

f (x) = \frac{27}{x ^{2} - 4 x - 5}

f (x) = \frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 2 x = \frac{4}{3}

y = x^{5} - x^{4}