Question

Find the intervals in which the function
fgiven by
f(x) = sinx+ cosx, 0x≤2π
is strictly increasing or strictly decreasing

Answer 1

I have no clue how to do this lol

Answer 2

Thankyou madam

Answer 3

youre welcome, sorry.

Answer 4

f'(x) = (sin x + cos x)'

f'(x) = cos x - sin x

We'll put f'(x) = 0.

cos x - sin x = 0

cos x = sin x

We'll divide by cos x both sides and we'll get:

sin x/cos x = 1

tan x = 1

The tangent has the positive value 1 in the 1st and 3rd quadrants.

x = pi/4 (1st quadrant)

x = pi + pi/4

x = 5pi/4 (3rd quadrant)

The extreme points of the function are:

f(pi/4) = sin pi/4 + cos pi/4 = 2sqrt2/2 = sqrt2

f(5pi/4) = sin pi/4 + cos pi/4 = -2sqrt2/2 = -sqrt2

The critical points of the function are x = pi/4 and x = 5pi/4 and the extreme points are (pi/4 ; sqrt2) and (5pi/4 ; -sqrt2).
@goformit100

Answer 5

Thankyou @LilySwan Madam