Final answer:
To find the values of x for which the slope of the curve y=f(x) is 0, solve for x in f'(x)=0.
Step-by-step explanation:
To find the values of x for which the slope of the curve y=f(x) is 0, we need to set the derivative of f(x) equal to 0. The derivative gives us the slope of the curve at any given point. So, we solve the equation f'(x)=0 to find x.
Let's assume the function f(x) is differentiable. After finding the derivative f'(x), we equate it to 0 and solve for x using algebraic methods. The resulting values of x will be the points where the slope of the curve is 0.
For example, if f(x) = x^2, then f'(x) = 2x. Equating 2x to 0, we find x = 0.