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Popular Functions >

extreme f(x)=2x-4sin(x)

Solution

extreme points

f (x) = 2 x - 4 sin (x)

Solution

Minimum (\frac{π}{3} + 2 πn, 2 (\frac{π}{3} + 2 πn) - 4 sin (\frac{π}{3} + 2 πn)), Maximum (\frac{5 π}{3} + 2 πn, 2 (\frac{5 π}{3} + 2 πn) - 4 sin (\frac{5 π}{3} + 2 πn))

Solution steps

Find the critical points:

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Domain of

2 x - 4 sin (x) : - \infty < x < \infty

Find intervals:

Decreasing

: 2 πn \leq x < \frac{π}{3} + 2 πn,

Increasing

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

Decreasing

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

Plug the extreme point

x = \frac{π}{3} + 2 πn

into

2 x - 4 sin (x) \Rightarrow y = 2 (\frac{π}{3} + 2 πn) - 4 sin (\frac{π}{3} + 2 πn)

Minimum (\frac{π}{3} + 2 πn, 2 (\frac{π}{3} + 2 πn) - 4 sin (\frac{π}{3} + 2 πn))

Plug the extreme point

x = \frac{5 π}{3} + 2 πn

into

2 x - 4 sin (x) \Rightarrow y = 2 (\frac{5 π}{3} + 2 πn) - 4 sin (\frac{5 π}{3} + 2 πn)

Maximum (\frac{5 π}{3} + 2 πn, 2 (\frac{5 π}{3} + 2 πn) - 4 sin (\frac{5 π}{3} + 2 πn))

Minimum (\frac{π}{3} + 2 πn, 2 (\frac{π}{3} + 2 πn) - 4 sin (\frac{π}{3} + 2 πn)), Maximum (\frac{5 π}{3} + 2 πn, 2 (\frac{5 π}{3} + 2 πn) - 4 sin (\frac{5 π}{3} + 2 πn))

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=2x-4sin(x) ?
The extreme f(x)=2x-4sin(x) is