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Popular >

extreme f(x)=2x-6sin(x)

Solution

extreme points

f (x) = 2 x - 6 sin (x)

Solution

Minimum (arccos (\frac{1}{3}) + 2 πn, 2 (arccos (\frac{1}{3}) + 2 πn) - 6 sin (arccos (\frac{1}{3}) + 2 πn)), Maximum (2 π - arccos (\frac{1}{3}) + 2 πn, 2 (2 π - arccos (\frac{1}{3}) + 2 πn) - 6 sin (2 π - arccos (\frac{1}{3}) + 2 πn))

Solution steps

Find the critical points:

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

Domain of

2 x - 6 sin (x) : - \infty < x < \infty

Find intervals:

Decreasing

: 2 πn \leq x < arccos (\frac{1}{3}) + 2 πn,

Increasing

: arccos (\frac{1}{3}) + 2 πn < x < 2 π - arccos (\frac{1}{3}) + 2 πn,

Decreasing

: 2 π - arccos (\frac{1}{3}) + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = arccos (\frac{1}{3}) + 2 πn

into

2 x - 6 sin (x) \Rightarrow y = 2 (arccos (\frac{1}{3}) + 2 πn) - 6 sin (arccos (\frac{1}{3}) + 2 πn)

Minimum (arccos (\frac{1}{3}) + 2 πn, 2 (arccos (\frac{1}{3}) + 2 πn) - 6 sin (arccos (\frac{1}{3}) + 2 πn))

Plug the extreme point

x = 2 π - arccos (\frac{1}{3}) + 2 πn

into

2 x - 6 sin (x) \Rightarrow y = 2 (2 π - arccos (\frac{1}{3}) + 2 πn) - 6 sin (2 π - arccos (\frac{1}{3}) + 2 πn)

Maximum (2 π - arccos (\frac{1}{3}) + 2 πn, 2 (2 π - arccos (\frac{1}{3}) + 2 πn) - 6 sin (2 π - arccos (\frac{1}{3}) + 2 πn))

Minimum (arccos (\frac{1}{3}) + 2 πn, 2 (arccos (\frac{1}{3}) + 2 πn) - 6 sin (arccos (\frac{1}{3}) + 2 πn)), Maximum (2 π - arccos (\frac{1}{3}) + 2 πn, 2 (2 π - arccos (\frac{1}{3}) + 2 πn) - 6 sin (2 π - arccos (\frac{1}{3}) + 2 πn))

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f (x) = - x^{2} - 7 y^{2} + 9 x - 6 y + 2

extreme (3x)/(sqrt(x-8))extreme points

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=2x-6sin(x) ?
The extreme f(x)=2x-6sin(x) is