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Popular >

extreme f(x)=x-2cos(x)

Solution

extreme points

f (x) = x - 2 cos (x)

Solution

Maximum (\frac{7 π}{6} + 2 πn, \frac{7 π}{6} + 2 πn - 2 cos (\frac{7 π}{6} + 2 πn)), Minimum (\frac{11 π}{6} + 2 πn, \frac{11 π}{6} + 2 πn - 2 cos (\frac{11 π}{6} + 2 πn))

Solution steps

Find the critical points:

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Domain of

x - 2 cos (x) : - \infty < x < \infty

Find intervals:

Increasing

: 2 πn \leq x < \frac{7 π}{6} + 2 πn,

Decreasing

: \frac{7 π}{6} + 2 πn < x < \frac{11 π}{6} + 2 πn,

Increasing

: \frac{11 π}{6} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{7 π}{6} + 2 πn

into

x - 2 cos (x) \Rightarrow y = \frac{7 π}{6} + 2 πn - 2 cos (\frac{7 π}{6} + 2 πn)

Maximum (\frac{7 π}{6} + 2 πn, \frac{7 π}{6} + 2 πn - 2 cos (\frac{7 π}{6} + 2 πn))

Plug the extreme point

x = \frac{11 π}{6} + 2 πn

into

x - 2 cos (x) \Rightarrow y = \frac{11 π}{6} + 2 πn - 2 cos (\frac{11 π}{6} + 2 πn)

Minimum (\frac{11 π}{6} + 2 πn, \frac{11 π}{6} + 2 πn - 2 cos (\frac{11 π}{6} + 2 πn))

Maximum (\frac{7 π}{6} + 2 πn, \frac{7 π}{6} + 2 πn - 2 cos (\frac{7 π}{6} + 2 πn)), Minimum (\frac{11 π}{6} + 2 πn, \frac{11 π}{6} + 2 πn - 2 cos (\frac{11 π}{6} + 2 πn))

Popular Examples

extreme f(x)=(x^2)/(x^2+4)extreme points

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

extreme f(x)=x^{1/3}+2x^{4/3}extreme points

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

extreme f(x)=x^3-2x^2+4 extreme points

f (x) = x^{3} - 2 x^{2} + 4

extreme f(x)=(4x)/(x^2+9),-4<= x<= 4 extreme points

f (x) = \frac{4 x}{x ^{2} + 9}, - 4 \leq x \leq 4

extreme-3(x+5)^3 extreme points

- 3 (x + 5)^{3}

Frequently Asked Questions (FAQ)

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