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Popular Functions >

extreme f(x)=2x-3sin(x)

Solution

extreme

Solution

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

Solution steps

Find the critical points:

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

Domain of

2 x - 3 sin (x) : - \infty < x < \infty

Find intervals:

Decreasing

: 2 πn \leq x < arccos (\frac{2}{3}) + 2 πn,

Increasing

: arccos (\frac{2}{3}) + 2 πn < x < 2 π - arccos (\frac{2}{3}) + 2 πn,

Decreasing

: 2 π - arccos (\frac{2}{3}) + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = arccos (\frac{2}{3}) + 2 πn

into

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

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

Plug the extreme point

x = 2 π - arccos (\frac{2}{3}) + 2 πn

into

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

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

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

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=2x-3sin(x) ?
The extreme f(x)=2x-3sin(x) is