1. Let f(x) be a function that is differentiable everywhere and has a derivative f'(x)=4x^2-4x+2. Verify that the Intermediate Value Theorem for Derivatives applies to the functionf'(x) on the interval [0,2], and find the value of C guaranteed by the theorem such that f'(c)=5
2. Use the fundamental definition of a derivative to find f'(x) where f(x)=x+a/x+b
3. Find the equation of the line tangent to the curve defined by f(x)=x^2+1/sqrt x at the point (1,2)
4. The locationxof a car in meters is given by the function x=30t-5t^2 wheretis in seconds. At the time when the car is moving at 10 m/s in the direction opposite to its initial motion, how far is the car from where it was att= 0?
5. The instantaneous rate of change of the volumeVof a sphere with respect to its radiusrcan be expressed as dV/dR= aV/r What isa? Recall that the volume formula for a sphere is V=4/3 pi*r^3
6. What is f''(pi/4), where f(x)=sin x+cos x?