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

on the interval[0,/2]

using the Extreme Value Theorem and the following steps,

1.f'(t)=

2. The value of0t/2

which makesf'(t)=0

is,

t₀=

3. Using the value oft₀

found in step 2., determinef(t₀)=

4. Determine the function value at the specified endpoints,

f(0)=

f(/2)=

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

Absolute Maximum:

Absolute Minimum: