(a) How can i find the intervals on which f is increasing or decreasing?
(b) local max and min.
f(x)=sin(x)+cos(x), 0≤x≤2(pi)
+130536 f(x) = sinx + cosx take the derivative and set to 0
f ' (x) = cosx - sinx = 0
So
cosx = sin x an this happens at pi/4 and 5pi/4 on 0≤x≤2(pi)
Take the second derivative
f " (x) = -sinx - cosx
Substituting in the critical points we have
-sin(pi/4) - cos(pi/4) = negative..... so we have a relative max at pi/4
And
-sin (5pi/4) - cos (5pi/4) = positive....... so we have a relative minimum at 5pi/4
So the function is increasing on [0, pi/4], decreasing on [pi/4, 5pi/4] and increasing again on [ 5pi/4, 2pi]
Here's a graph [ in degrees]...........https://www.desmos.com/calculator/r1e6o1daoa
+130536 f(x) = sinx + cosx take the derivative and set to 0
f ' (x) = cosx - sinx = 0
So
cosx = sin x an this happens at pi/4 and 5pi/4 on 0≤x≤2(pi)
Take the second derivative
f " (x) = -sinx - cosx
Substituting in the critical points we have
-sin(pi/4) - cos(pi/4) = negative..... so we have a relative max at pi/4
And
-sin (5pi/4) - cos (5pi/4) = positive....... so we have a relative minimum at 5pi/4
So the function is increasing on [0, pi/4], decreasing on [pi/4, 5pi/4] and increasing again on [ 5pi/4, 2pi]
Here's a graph [ in degrees]...........https://www.desmos.com/calculator/r1e6o1daoa
