Assignment:
Q1. If f(x) = ln(sin(x^2)), then f''(x)=? Explain.
Q2. The college is making parking lot, rectangular and enclose 6000 sq meters. A fence will surround the lot and on parallel to one of the sides will divide the lot into two sections. What are the dimensions in meters of the rectangle lot using the least amount of fencing? Explain.
Q3. Let f(x) = x^3 + x. If h is the inverse function of f then h'(20) equals?
Q4. A spherical balloon is inflated. At a rate of 25cm^3/sec. At what rate in cm/sec is the radius of the balloon changing when the radius is 2cm?
Provide complete and step by step solution for the question and show calculations and use formulas.