Posted by **bob** on Sunday, November 4, 2012 at 10:44pm.

I need to use calculus to solve this word problem:

Find all maximum and minimum values for f(x)= sin(x)+ cos(x) on [0, 2(3.14)]

How do I do it?

- math -
**Reiny**, Monday, November 5, 2012 at 12:31am
f(x) = sinx + cosx , 0 ≤ x ≤ 2π

f ' (x) = cosx - sinx

= 0 for a max/min

cosx - sinx = 0

sinx = cosx

sinx/cosx = 1

tanx = 1

x = 45° or 225°

x = π/4 or x = 5π/4

f(π4) = √2/2 + √2/2 = √2

f(5) = -√2/2 - √2/2 = -√2

the max is √2, the min is -√2

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