The maximum value of F in F(x) = - 4 cos x is 2 4 1

Consider the function f(x) = 6x + 12 sin x on the domain [0, 2π]. Use analytic techniques (calculus, algebra, trigonometry) to determine the intervals where the function is increasing and decreasing. Use exact values in your response. f(x) is increasing on f(x) is decreasing on

Find F as a function of x and evaluate it at x = 0, x = T/4, and x = T/2. F(x) cos 0 do F(x) F(0)

Find and verify the operator that annihilates the function f(x)=e-²x sinx

Let f′′(θ)=sin(θ)+cos(θ) and suppose that f(0)=6 and f′(0)=10.  What is the sum of the coefficients on all 4 terms in f(θ)?