+956 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?
+9466 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.
+9466 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.
