Let f(x) = 4 sin x
Complete parts (a) through (e) below
a. What is the y-intercept of the graph of f?
b. For what numbers x, -π ≤ x ≤ π, is the graph of f increasing?
a. The y-intercept of a function is the value of the function when x is equal to 0. Therefore, to find the y-intercept of f(x) = 4 sin x, we substitute x = 0 into the function:
f(0) = 4 sin 0 = 4(0) = 0
So the y-intercept of the graph of f is 0.
b. The graph of f(x) = 4 sin x is increasing when the derivative of the function is positive. To find the derivative of f(x), we differentiate with respect to x:
f'(x) = 4 cos x
Now, we want to find the values of x for which f'(x) > 0. Since cos x is positive in the interval -π/2 ≤ x ≤ π/2, we can say that f(x) is increasing when -π/2 ≤ x ≤ π/2.
Therefore, for the numbers x in the interval -π ≤ x ≤ π, the graph of f is increasing when -π/2 ≤ x ≤ π/2.