Question
Asked Dec 2, 2019
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Consider the function on the interval (0, 2π).

Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)

increasing :

decreasing :

Apply the First Derivative Test to identify the relative extrema.

relative maximum :

relative minimum :

sin(x)
f(x)
4 +(cos(x))2
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sin(x) f(x) 4 +(cos(x))2

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Expert Answer

Step 1

Given, function is

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sin(x) f(x)= -(1) 4+(cos(x))

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Step 2

For critical points of function, differentiate function and equal to zero.

Differentiate equation (1) with respect to ‘x’,

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sin (x) d (x)= dx4cos(x d )(4+cos'(x)) (4+cos (x)sin (x)- sin(x) (4+cos" (x)) _ du u'v-и-v" dx dx dxv cos(x)(4+cos (x))-sin (x)(-2cos(x)sin (x)) (4+cos (x)) cos(x)(4 cos (x))+ sin(x)sin(2x) 4+cos2 (x)

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Step 3

Take derivative is e...

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cos(x)(4+cos (x))+ sin (x)sin(2x) (4+cos (x) = 0

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Tagged in

Math

Calculus

Derivative