Posted by **rudy** on Thursday, May 15, 2008 at 8:22pm.

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

- math -
**Reiny**, Friday, May 16, 2008 at 1:29am
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.

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