Absolute maxima and minima Determine the location and value of

rastafarral6

rastafarral6

Answered question

2021-12-03

Absolute maxima and minima Determine the location and value of the absolute extreme value of f on the given interval, if they exist.
f(x)=secx on [π4,π4]

Answer & Explanation

hotcoal3z

hotcoal3z

Beginner2021-12-04Added 16 answers

Step 1
Given:
f(x)=secx [π4,π4]
Differentiate the function in order to find the critical points and then put the derivative equal to zero.
d(secx)dx=secxtanx
secxtanx=0
The only such value in the interval is x=0 so there is only one critical point to consider in the interval.
Step 2
Now, find the value of f(x) at 0, π4,π4
sec(0)=1
sec(π4)=1.42
sec(π4)=1.42
Maximum value is at f(π4)=1.42 and minimum value is at f(π4)=1.42
So, absolute maxima at f(π4) and absolute minima is at f(π4)

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