Given f(x)=sin(x)-2cos(x) on the interval [0,2pi].

Question

a) Determine where the function is increasing and decreasing.
b) Determine where the function is concave up and concave down.
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I know:

f′(x)=cos(x)+2sin(x)
f″(x)=-sin(x)+2cos(x)

Other than that^^ I have no clue how to get the intervals where the function is increasing/decreasing and where it's concave up/concave down.

Answer 1

Go back and review he subject.

The function is increasing where f' > 0
The curve is concave up where f'' > 0.

Now just check 'em out.