Rutgers University-Camden 640:121 Calculus I Test 2 Review Questions 1. Use the limit definition of the derivative to find the equation of the line tangent to the graph of f(x)=2x-1 when x = 5. 1 where f(x) 0 and is differentiable for any x. 2. Suppose g(x) = (f(x)) (a) Use the limit definition of the derivative to find a formula for g'(x) (in terms of f and f'). (b) Based on your answer from (a), find the value of g'(3) if f(3) = 2 and f'(3) = 12. 3. Let f(x)=log(2 +17). (a) Show that f(x) has a critical point at x = 0. (b) Find the equation of the line tangent to the graph of y = f(x) at x = 4. 4. Find y' if y = cos(cos z)) 5. Find h'(x) if h(x)=7(tan) (Note: the whole expression (rtanr) is in the power). 6. Use implicit differentiation to find the equation of the line tangent to 2+ = y+3 at the point (1,1). 7. Let f(t)=(8-t) on I = [0,8]. State that the Extreme Value Theorem applies in this case, then find the absolute maximum and minimum of f on I.