+0  
 
0
44
1
avatar+910 

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?

Julius  Apr 25, 2018

Best Answer 

 #1
avatar+7048 
+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.

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

1+0 Answers

 #1
avatar+7048 
+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

22 Online Users

avatar
New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy