Asked by Mark
maximum and minimum of y = cos(x) + sin (x)on the interval [0,2pi]
Answers
Answered by
MathMate
Let
f(x) = cos(x) + sin (x)
Calculate derivative f'(x) and equate to zero. Solve for x.
For each value x1 of the solution, verify
f''(x). f''(x)<0 = maximum, and f''(x)>0 = minimum.
There may be multiple maxima and minima, choose the extreme values.
f(x) = cos(x) + sin (x)
Calculate derivative f'(x) and equate to zero. Solve for x.
For each value x1 of the solution, verify
f''(x). f''(x)<0 = maximum, and f''(x)>0 = minimum.
There may be multiple maxima and minima, choose the extreme values.
Answered by
Tom
would the max be sqrt(2) at x = pi/4, and the min be -sqrt(2) at x = 5pi/4?
Answered by
MathMate
Exactly! where tan(x)=1.
Answered by
Tom
thank you very much
Answered by
MathMate
You're welcome!
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