Final answer:
To find the critical points of the function y = tan(px/20) on the interval [0,5], we first take the derivative using the chain rule, set it equal to zero, and solve for x. We find that there are no critical points on the interval [0,5].
Step-by-step explanation:
To find the critical points of the function y = tan(px/20) on the interval [0,5], we need to first find the derivative of the function and then set it equal to zero to solve for x.
Step 1: Take the derivative of the function using the chain rule. The derivative of tan(px/20) is p/20 * sec^2(px/20).
Step 2: Set the derivative equal to zero and solve for x. p/20 * sec^2(px/20) = 0. Since the term p/20 is nonzero, we can cancel it out, leaving us with sec^2(px/20) = 0. This equation has no real solutions.
Therefore, there are no critical points on the interval [0,5].