Chapter 4, Problem 46RE

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Finding Points of Inflection In Exercises 41-48, find the points of inflection and discuss the concavity of the graph of the function. f ( x ) = tan x 4 ,       ⌈ 0 , 2 π ⌉

To determine

To calculate: The points of inflection for the function f(x)=tanx4 over the interval (0,2π) and thus its concavity.

Explanation

Given:

The function f(x)=tanx4 over the interval (0,2Ï€).

Formula Used:

The inflection point of the function corresponds to the point where its second derivative disappears.

For a function f that is twice differentiable on an open interval I:

If f''(x)>0 for all x in I, the function f is concave upwards on I and if f''(x)<0 for all x in I, the function f is concave downwards on I.

Calculation:

Now differentiate the provided function twice.

f'(x)=14sec2x4f''(x)=14(2secx4)(14)(secx4tanx4)=18sec2x4tanx4

Equate the second derivative to zero to obtain the inflection point

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