find the local max and min values of f(x)=xsinx+cosx for

**-pi≤x≤pi**I am so stuck at how to figuring out the sign, which is important. I did take the derivative xcosx=0 then x=0 and cosx0

Please help!

find the local max and min values of f(x)=xsinx+cosx for **-pi≤x≤pi**

I am so stuck at how to figuring out the sign, which is important. I did take the derivative xcosx=0 then x=0 and cosx0

Please help!

Tutors, please sign in to answer this question.

Mesa, AZ

f' = xcosx = 0 if x={±π/2, 0} ...three critical points to locate local extrema.

Arranging the three critical points on a number-line that goes from -π to π, we see that there are several intervals to consider.

The leftmost interval is (-π, π/2) and during that interval f' is positive so f is increasing;

on (-π/2,0) f' is negative so f is decreasing;

on (0, π/2) f' is positive so f is increasing;

on (π/2,π) f' is negative so f is decreasing.

These facts mean that there's a local MIN when x=0, and local MAX at ±π/2.

East Elmhurst, NY

f'(x) = 0

sinx + xcosx - sinx = 0

xcosx = 0

x = 0 cosx = 0

The interval indicates that you start on the negative x-axis, then rotate clockwise 2π on the unit circe.

x = -π/2 x = π/2

Your local max and min occur at these two x values. You can take it from here.

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