1. If f (4) = 5 and g(x) = 2f(3x) evaluate g' (3) 2. Write the exact local linearization to the curve f (x) = arctan(x) +- at x = 1. (You will need to evaluate the arctangent function to its exact value.) 3. Write the logarithmic function with no product, division, or exponents inside the function. In 2 3Vx 4. Find the derivative of the following continuous piecewise function,,T(w). Place your answers on the blanks provided. Justify using calculus the derivatives at x = 0 and x = 0.5. (Not a graphic approach.) You must evaluate the trig functions to their exact value. sin(w) + w W 0.5 5. Find the derivative of y = sin(x4) + sin2(rx) + 3xsin(x) + sin(3x + 1) + ent (No simplification is required) 6. Given f(t) = arcsin(t3 - t) find ar. 7. Let f(x) = In(x). Find the exact value of c such that f' (c) = f(e)-f(1) e-1 8. If k 2 1, the graphs of f (x) = sin(x) and g(x) = ke * intersect for x 2 0. Find the smallest k for which the graphs are tangent. What are the coordinates of the point of tangency