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

#1**+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

#1**+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