1. Find the following derivatives.

(a) y=4x^5-x*\sqrt{x}, dy/dx=?

(b) y= (2+cos(x/3)/(x^2), dy/dx=?

(c) f(x)=(-x+4)*(x^4+cos(x))

2. Use the limit defn of f'(x) to verify that f'(2)=11 if f(x)=x^3-x.

3. Find the equation of the tangent line to the graph y=x^2+1/x at (1,2).

4. Find the instantaneous velocity at t=Pi/4 of a particle whose position at time t is s(t)= 4cos^2(t).

5. Find the lim_{t->\infty} (t^3+\sqrt(t))/(t+sin(t)-t^3)

6. True of False (You must give at least one reason for your answer in a complete sentence. An answer alone is worth zero.)

(a) If f(x)>0 for all x and is differentiable for all x, then f'(x)>0 for all x.

(b) If f(x) and g(x) are both not continuous at x=0, then f(x)+g(x) is not continuous at x=0.