Question

I got the previous question I was trying to figure out related to this, but as soon as it included Trig I got lost!!! please help the question is:

Consider the equation below.
f(x) = 5 sin x + 5 cos x, 0 ≤ x ≤ 2π

A)(a) Find the interval on which f is increasing. (Enter your answer using interval notation.)
Find the interval on which f is decreasing. (Enter your answer using interval notation.)

(b) Find the local minimum and maximum values of f.
(c) Find the inflection points
(x,y)=( , ) smaller x-value
(x,y)=( , ) larger x-value
Find the interval on which f is concave up/down

Answer 1

@stan2244 Are you still here?

Answer 2

Welp, I'll just right out your start. Find the derivative of the function, which is a simple derivative. So we have f'(x). An application of the derivative is that we can find out the slope of the tangent line at any point. So, that means when f'(x) is positive, the corresponding x-coordinates have a positive slope. Thus, whenever f'(x) is positive, f(x) is increasing.

Answer 3

And the opposite is true. When f'(x) is negative on some interval, f(x) is decreasing on that open interval.