Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
d. The lines tangent to the graph of y=sin x on the interval [−π/2,π/2] have a maximum slope of 1.

Verified step by step guidance

1. Identify the function given in the problem, which is y = sin(x), and understand that we need to analyze its behavior on the interval [−π/2, π/2].
2. Calculate the derivative of the function, y' = cos(x), to find the slope of the tangent lines at any point x on the graph.
3. Evaluate the derivative at the endpoints of the interval and at critical points to determine the maximum slope. The critical points occur where the derivative is zero or undefined.
4. Check the values of the derivative at x = −π/2, x = 0, and x = π/2 to see if the maximum slope of the tangent lines is indeed 1.
5. Conclude whether the statement is true or false based on the maximum value of the derivative found in the previous step and provide a brief explanation or counterexample if necessary.