Question

using the interval [0,2pi]
and f(x) = sinx + cosx, obtain c £ (0,2pi) that satisfies the conclusion of Rolle's theorem
where £ mean element of and C means number
show step

Answer 1

f(0) = f(2π) = 1
so the condition is satisfied.

So, now you want c such that f'(c)=0

f' = cosx - sinx
f' = 0 at x = π/4
π/4 is in the interval [0,2π], so ta-da!