If a *, show work. If a @, set up and write the answer (essentially, show a meaningful step). If a +, round to 100th (exact is OK if it's simpler). Always, simplify as much as possible. 1. (8 pts.) Consider v16.1 (which we will want to estimate). a. Determine the function, f (x). @b. Find f'(x) f ( x ) = X F (z) = c. Determine a so that f(a) = v16.1. 1% d. Determine f (d). @f. Use b - d to approximate v16.1. Round to the 100th. LLX ) = fla) (x - a ) + f(a) L (b. 1) = ( 16-1 - 16)+ 4 4.01 2. (8 pts.) The height of an object / seconds after it is thrown upward in meters is h(t) = -4.9+2 + 21t + 2 @a. Find the average velocity @b. The Mean Value Theorem verifies that, at some of the object from 1 to 4 time during the from 1 to 4 seconds, the seconds. instantaneous velocity equals the average velocity. h(4) - h(o) Find that time. average velocity a dt = - 9.8 +21 4 - 0 1.4 :-9.8t + 21 : 1. 4 m /sec 9 8t = 19. 6 t = 1 03. (22 pts.) Consider the equation y = x(/) (x30). a. Sketch a graph of the equation. *b. Evaluate the derivative of the equation. (Hint: Jim * = 00.) be In y @c. What is the slope of the tangent line at x = 3. Round to the 100". d. Find the equation of the tangent line at x = 3. Round to the 100". (Put it in y = mx +6 form). Sketch it on the same graph as a. +@e. Where is the minimum (the x-value)? @4. (12 pis.) Find the derivative of y = 2tan "[In(x)]. (Represent as ONE fraction)