Calculus - Trigonometry

Question

The curve y = sin(x) + cos(x) has two points where the tangent line is horizontal on the interval . The y co-ordinates of these points is the positive and negative square root of a positive integer. What is this integer?

Answer 1

2

sin x + cos x = √2 sin(x + π/4), which has a maximum of √2 at π/4 and a minimum of -√2 at 5π/4