calculus Question

Question

Use the function f(x) = sinx+cosx, where 0≤x≤pi, to answer the following.

A) Determine all stationary points. Classify the points as relative minima or maxima.
B) Locate any points of inflection.
C) Determine the endpoints of the interval and sketch the graph.

Help!?

Answer 1

this is a duplicated submission...the two identical questions appear in adjacent positions on the screen.

The other one has been answered.

Answer 2

f(x) = sinx+cosx, where 0≤x≤pi

f'(x) = cos x - sin x

f' = 0 if cos x = sin x which occurs when x = pi/4.  

Therefore (pi/4,√2) is a stationary (critical) point.

f"(x) = -sin x - cos x and therefore f"(crit pt) is negative and thus the stationary point is a relative maximum.

f" = 0 if sin x = - cos x. This occurs when x = ¾(pi). That would be where the inflection point is.