SOLUTION: Find and classify the stationary points of the function y(x) = sin x + cos x on the interval 0 ≤ x ≤ π. Find the points of inflection.

Algebra ->  Average -> SOLUTION: Find and classify the stationary points of the function y(x) = sin x + cos x on the interval 0 ≤ x ≤ π. Find the points of inflection.      Log On


   

Question 1098868: Find and classify the stationary points of the function y(x) = sin x + cos x on the interval 0 ≤ x ≤ π.
Find the points of inflection.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
To find the stationary points, take the derivative and set it equal to zero.
dy%2Fdx=cos%28x%29-sin%28x%29=0
cos%28x%29=sin%28x%29
x=%281%2F4%29pi
.
.
.
To find the inflection points, take the second derivative and set it equal to zero.
d2y%2Fdx2=-sin%28x%29-cos%28x%29=-%28sin%28x%29%2Bcos%28x%29%29=0
sin%28x%29=-cos%28x%29
x=%283%2F4%29pi