What is the extreme f(x)=cos(5x)+sqrt(3)sin(5x) ?

The extreme f(x)=cos(5x)+sqrt(3)sin(5x) is

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Popular >

extreme f(x)=cos(5x)+sqrt(3)sin(5x)

Solution

extreme points

f (x) = cos (5 x) + 3 sin (5 x)

Solution

Maximum (\frac{π}{15} + 2 πn, 2), Minimum (\frac{4 π}{15} + 2 πn, - 2), Maximum (\frac{7 π}{15} + 2 πn, 2), Minimum (\frac{2 π}{3} + 2 πn, - 2), Maximum (\frac{13 π}{15} + 2 πn, 2), Minimum (\frac{16 π}{15} + 2 πn, - 2), Maximum (\frac{19 π}{15} + 2 πn, 2), Minimum (\frac{22 π}{15} + 2 πn, - 2), Maximum (\frac{5 π}{3} + 2 πn, 2), Minimum (\frac{28 π}{15} + 2 πn, - 2)

Solution steps

Find the critical points:

x = \frac{π}{15} + 2 πn, x = \frac{4 π}{15} + 2 πn, x = \frac{7 π}{15} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{13 π}{15} + 2 πn, x = \frac{16 π}{15} + 2 πn, x = \frac{19 π}{15} + 2 πn, x = \frac{22 π}{15} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{28 π}{15} + 2 πn

Domain of

cos (5 x) + 3 sin (5 x) : - \infty < x < \infty

Find intervals:

Increasing

: 2 πn \leq x < \frac{π}{15} + 2 πn,

Decreasing

: \frac{π}{15} + 2 πn < x < \frac{4 π}{15} + 2 πn,

Increasing

: \frac{4 π}{15} + 2 πn < x < \frac{7 π}{15} + 2 πn,

Decreasing

: \frac{7 π}{15} + 2 πn < x < \frac{2 π}{3} + 2 πn,

Increasing

: \frac{2 π}{3} + 2 πn < x < \frac{13 π}{15} + 2 πn,

Decreasing

: \frac{13 π}{15} + 2 πn < x < \frac{16 π}{15} + 2 πn,

Increasing

: \frac{16 π}{15} + 2 πn < x < \frac{19 π}{15} + 2 πn,

Decreasing

: \frac{19 π}{15} + 2 πn < x < \frac{22 π}{15} + 2 πn,

Increasing

: \frac{22 π}{15} + 2 πn < x < \frac{5 π}{3} + 2 πn,

Decreasing

: \frac{5 π}{3} + 2 πn < x < \frac{28 π}{15} + 2 πn,

Increasing

: \frac{28 π}{15} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{15} + 2 πn

into

cos (5 x) + 3 sin (5 x) \Rightarrow y = 2

Maximum (\frac{π}{15} + 2 πn, 2)

Plug the extreme point

x = \frac{4 π}{15} + 2 πn

into

cos (5 x) + 3 sin (5 x) \Rightarrow y = - 2

Minimum (\frac{4 π}{15} + 2 πn, - 2)

Plug the extreme point

x = \frac{7 π}{15} + 2 πn

into

cos (5 x) + 3 sin (5 x) \Rightarrow y = 2

Maximum (\frac{7 π}{15} + 2 πn, 2)

Plug the extreme point

x = \frac{2 π}{3} + 2 πn

into

cos (5 x) + 3 sin (5 x) \Rightarrow y = - 2

Minimum (\frac{2 π}{3} + 2 πn, - 2)

Plug the extreme point

x = \frac{13 π}{15} + 2 πn

into

cos (5 x) + 3 sin (5 x) \Rightarrow y = 2

Maximum (\frac{13 π}{15} + 2 πn, 2)

Plug the extreme point

x = \frac{16 π}{15} + 2 πn

into

cos (5 x) + 3 sin (5 x) \Rightarrow y = - 2

Minimum (\frac{16 π}{15} + 2 πn, - 2)

Plug the extreme point

x = \frac{19 π}{15} + 2 πn

into

cos (5 x) + 3 sin (5 x) \Rightarrow y = 2

Maximum (\frac{19 π}{15} + 2 πn, 2)

Plug the extreme point

x = \frac{22 π}{15} + 2 πn

into

cos (5 x) + 3 sin (5 x) \Rightarrow y = - 2

Minimum (\frac{22 π}{15} + 2 πn, - 2)

Plug the extreme point

x = \frac{5 π}{3} + 2 πn

into

cos (5 x) + 3 sin (5 x) \Rightarrow y = 2

Maximum (\frac{5 π}{3} + 2 πn, 2)

Plug the extreme point

x = \frac{28 π}{15} + 2 πn

into

cos (5 x) + 3 sin (5 x) \Rightarrow y = - 2

Minimum (\frac{28 π}{15} + 2 πn, - 2)

Maximum (\frac{π}{15} + 2 πn, 2), Minimum (\frac{4 π}{15} + 2 πn, - 2), Maximum (\frac{7 π}{15} + 2 πn, 2), Minimum (\frac{2 π}{3} + 2 πn, - 2), Maximum (\frac{13 π}{15} + 2 πn, 2), Minimum (\frac{16 π}{15} + 2 πn, - 2), Maximum (\frac{19 π}{15} + 2 πn, 2), Minimum (\frac{22 π}{15} + 2 πn, - 2), Maximum (\frac{5 π}{3} + 2 πn, 2), Minimum (\frac{28 π}{15} + 2 πn, - 2)

Popular Examples

inverse of f(x)=\sqrt[5]{x-1}inverse

domain of f(x)=(x-3)/(x^2-x-2)domain

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

extreme 2x^2-x-1 extreme points

2 x^{2} - x - 1

critical f(x)=e^xsqrt(x)critical points

f (x) = e^{x} x

asymptotes of f(x)=(x^2+4)/(x-2)asymptotes

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

Frequently Asked Questions (FAQ)

What is the extreme f(x)=cos(5x)+sqrt(3)sin(5x) ?
The extreme f(x)=cos(5x)+sqrt(3)sin(5x) is