Question

Find tha maximum value of sinx+cosx?

Answer 1

`"max"`:

`x = pi/4 + 2pin`.
`y = sin(pi/4) + cos(pi/4) = 2/sqrt(2) = sqrt(2)`

Explanation:

The first derivative is given by

`f'(x) = cosx - sinx`

Which will have critical numbers at

`0 =cosx - sinx`

`sinx =cosx`

So when `x= pi/4` and `x = (5pi)/4`. At `x =0`. the derivative has value `f'(0) = cos(0) - sin(0) = 1`, therefore the function is increasing at `x = 0` and `x = pi/4` is a maximum.

These maximums will happen at an interval of `2pi`, therefore the answer is `"max" = pi/4 + 2pin`.

Hopefully this helps!