Question

Find the values of x on the curve y = cos x 2 + sin x at which the tangent is horizontal. (let n be an integer. enter your answers as a comma-separated list.)

Answer 1

To find the values of x on the given curve at which the tangent is horizontal, we need to find the points where the derivative of y with respect to x is equal to 0.

Step-by-step explanation:

To find the values of x on the curve y = cos x^2 + sin x at which the tangent is horizontal, we need to find the points where the derivative of y with respect to x is equal to 0. The derivative of y is -2x sin x + cos x.

Setting the derivative equal to 0, we have -2x sin x + cos x = 0. Solving this equation will give us the values of x at which the tangent is horizontal.

Unfortunately, it is not possible to find exact solutions to this equation analytically. We can, however, solve it numerically using methods such as Newton's method or the bisection method.

Answer 2

y = cos^2(x) + sin(x)
y' = --2sin(x) + cos(x) = 0 first derivative. Set to 0 for horizontal tangent.
-2sin(x) = -cos(x)
Tan(x) = 1/2
x = 26.565 degrees