math
posted by rudy on .
Sketch
f (x) = x + cos x on
[2pie,2pie ]. Find any local extrema, inflection points, or asymptotes. And find the absolute maximum and absolute minimum values of f on the given interval.
i cant seem to figure out how to solve this

for local extrema f'(x) = 0
1  sinx = 0
sinx=1
x = pi/2 or 3pi/2 for the given domain
f(pi/2) = pi/2 + cos(pi/2) = pi/2 + 0 = pi/2
for x=3pi/2 f(3pi/2) = 3pi/2
so the local extrema are pi/2 and 3pi/2
inflection points : f''(x) = 0
cosx=0
x = ±pi/2 or ±3pi/2
sub those x values back into original to get the y of the points of inflection
consider the end points of the domain for absolute max/mins
f(2pi) = 2pi + cos(2pi) = 2pi + 1
f(2pi) = 2pi + 1
compare these with the local max/mins and use your calculator to determine the largest and smallest values
BTW, no asymptotes, the graph will be a cosine curve rising as x gets larger.