Find the absolute maximum and absolute minimum values of f on the given interval. f(t)=5t+5cot(t/2), [pi/4, 7pi/4] absolute minimum value-? absolute maximum value-?

Falak Kinney

Falak Kinney

Answered question

2020-10-28

Find the absolute maximum and absolute minimum values of f on the given interval.
f(t)=5t+5cot(t2),[π4,7π4]
absolute minimum value-?
absolute maximum value-?

Answer & Explanation

Margot Mill

Margot Mill

Skilled2020-10-29Added 106 answers

Step 1
Consider the given function
f(t)=5t+5cot(t2)
Step 2
Find the first derivative
f(t)=ddt(5t+5cot(t2))
=ddt(5t)+ddt(5cot(t2))
=552csc2(t2)
Step 3
Set the derivative equal to 0 to find the critical numbers
f'(t)=0
552csc2(t2)=0
csc2(t2)=2
csc(t2)=±2
t=π2,3π2for[π4,7π4]
Step 4
Evaluate f(t) at the endpoints and the obtained critical points.
f(π4)=5(π4)+5cot(π8)16
f(π2)=5(π2)+5cot(π4)12.85
f(3π2)=5(3π2)+5cot(3π4)18.56
f(7π4)=5(7π4)+5cot(7π8)15.42
Step 5
Therefore, the function f has
absolute minimum value 12.85
absolute maximum value 18.56

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?