Absolute Extrema

Question

Find the absolute extrema of the function f(t)=2cos(t)+sin(2t)

 on the interval [0,𝜋/2]

 using the Extreme Value Theorem and the following steps,

1. f'(t)=

 

 

2. The value of 0≤ t≤ 𝜋/2

 which makes f'(t)=0

 is,

t₀=

 

 

3. Using the value of t₀

 found in step 2., determine f(t₀)=

 

 

4. Determine the function value at the specified endpoints,

f(0)=

 

 

f(𝜋/2)=

 

 

5. Combining steps 3. and 4., and using the Extreme Value Theorem, we have that

Absolute Maximum: 

 

Absolute Minimum: 

 

Answer 1

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