Question

Determine the open intervals on which the graph is concave upward or concave downward. (Enter your...

Determine the open intervals on which the graph is concave upward or concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

y = 3x +

2
sin x

,    (−π, π)

Homework Answers

Answer #1

Solution:

Given

Differentiating with respect to x

Again differentiating with respect to x

Now find where y’’=0 or undefined in the interval [-π,π]

It is 0 in three places and there is no point in the interval at which it is undefined.

Now test the intervals determined by y’’=0 and find concavity based on the conditions if

y’’>0 means concave up

y’’<0 means concave down

Interval (-π,0):

Interval (0,π):

Hence for interval (-π,0) given function concaves up and for interval (0) it concaves down.

Graph confirms the concavity.

(Appreciate if found helpful)

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