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Which of the following is the maximum value of the function f(x) = 5tanx on the interval 0 ≤ x ≤ π/4? 

 

a) 0 

b) 5 

c) 10 

d) π 

 

I'm saying 0, am I correct?

 Apr 25, 2018

Best Answer 

 #1
avatar+7350 
+2

As  x  gets closer to  π/2  (from the left)  tan x  gets larger.

 

A line that is  π/2  radians with the positive  x  axis is a straight vertical line.

 

So to make  tan x  as large as possible, we want to make  x  as close to  π/2  as possible...

The closest that  x  can be within the domain is  π/4 .

 

When  x  = π/4 ,      f(x)  =  f(π/4)  =  5 tan( π/4 )  =  5(1)  =  5

 

If we look at a graph, here...

 

https://www.desmos.com/calculator/5g8sgfmwo7

 

we can see that the maximum value of  y   is  5 .

 

*edit*

 

We want  x  to  be as close to  π/2  as possible without going over. Once  x  goes past  π/2  the tangent becomes negative.

 Apr 25, 2018
edited by hectictar  Apr 26, 2018
 #1
avatar+7350 
+2
Best Answer

As  x  gets closer to  π/2  (from the left)  tan x  gets larger.

 

A line that is  π/2  radians with the positive  x  axis is a straight vertical line.

 

So to make  tan x  as large as possible, we want to make  x  as close to  π/2  as possible...

The closest that  x  can be within the domain is  π/4 .

 

When  x  = π/4 ,      f(x)  =  f(π/4)  =  5 tan( π/4 )  =  5(1)  =  5

 

If we look at a graph, here...

 

https://www.desmos.com/calculator/5g8sgfmwo7

 

we can see that the maximum value of  y   is  5 .

 

*edit*

 

We want  x  to  be as close to  π/2  as possible without going over. Once  x  goes past  π/2  the tangent becomes negative.

hectictar Apr 25, 2018
edited by hectictar  Apr 26, 2018

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