*SHOW ALL STEPS AND WORK*

1. Use the fundamental definition of a derivative to find f'(x) where f(x)=x+a/x+b
2. 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
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). Show all your work.