How do you determine if a function is

Jewel Beard

Jewel Beard

Answered question

2022-04-18

How do you determine if a function is concave up/ concave down if tanx+2x on (π2,π2)?

Answer & Explanation

resacarno4u

resacarno4u

Beginner2022-04-19Added 12 answers

Step 1
Investigate the sign of the second derivative.
Explanation:
Let: y=tanx+2x on (π2,π2)
y'=sec2x+2 (For finding y", remember that sec2x=(secx)2 so we'll use the chain rule)
y =2secxsecxtanx (The derivative of 2 is 0.)
So y2sec2xtanx.
y" is never undefined on (π2,π2), so its only chance to change sign is at its zero(s)..
|secx|1,so sec2x>1. So the only zero of y" is where tanx=0, which is at x=0.
Step 2
For x in (π2,0),tanx is negative, so y" is negative and the graph of the function is concave down.
For x in (0,02),tanx is positive, so y" is positive and the graph of the function is concave up.
The function is concave down on (π2,0), and it is concave up on (0,π2).
The point (0, 0) is an inflection point.

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