Derivatives and Optimization

Which rule is used to find the derivative of a constant term in a function? (K/U)

.(K/U)

Find the derivative of the funtion. (hint: you will need to multiply first!) (K/U)

(K/U)

How many derivatives can you take of a function?(T/I)

Find the slope at x = 3 of the equation f(x) = 3x²

(T/I)

Given the function f(x) = e^x * ln(x), find the critical points and determine whether each point is a local minimum, local maximum, or neither. Video record your answer. (C)

Write a persuasive argument about the importance of calculus in various fields, such as engineering, physics, and economics. (C)

Write a clear and detailed solution to the following problem: "A rocket is launched vertically upward from the ground. Its height in meters above the ground, t seconds after launch, is given by h(t) = 60t - 5t^2. Determine the maximum height reached by the rocket and the time it takes to reach that height." Voice records your steps for this question. (A)

A rectangular garden is to be fenced on three sides, with the fourth side being the wall of a house. If 200 meters of fencing is available, find the dimensions of the garden to maximize its area. (A)