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

A) when is f'(x)>0? when is f'(x)<0?
B) when is f'(x)=0? is f''(x)>0 (a minimum) or is f''(x)<0 (a maximum) at this point?
C) when is f''(x)=0? when is f''(x)>0 (concave up)? when is f''(x)<0 (concave down)?

Answer 2

Sorry for late response, let me look over what you just said.

Answer 3

I keep trying to work it out, I know 5cosx -5sinx=0 then does that somehow turn into 5tanx? @eashy

Answer 4

5cos(x)-5sin(x)=0
5sin(x)=5cos(x) <--divide by cos(x)
5tan(x)=5
tan(x)=1

Answer 5

so pi/4 and 5pi/4 at f' right? im still struggling on what to do from there?

Answer 6

wait, so its
increasing(0 , pi/4) , (5pi/4 , 7pi/4)
decreasing(pi/4 , 5pi/4) , (7pi/4 , 2pi)
now how do i find loc min and max of it?