You must show all of your work. Partial credit will be given. Calculators are allowed on this exam Problem 1. Let f(0) = 02 cos . (a) Find the lincar approximation of f(0) at 0 = T Proble (9)Make a Bit of all the c (b) Estimate f(3) using part (a). Problem 2. Use a lincar approximation to estimate the value of In (1.1) Problem 3. Find all critical values of the following function. f (t) = = t - 1 t 2 - t+ 142 Too You must show all your work. Partial credi 1. Solve the equation ? = 11x - 10 by f * 2- 1x - 10*+ 10 x - 11 x+ 10= 0 - 11 x +10 ( x - / Xx - > 1X = 19 x = 1 6x - 2 : 3 2 2 Solu z - 2= 3x2 using the quadrat Problem 4. Find all critical values of the following function. f() = re-3 using any method ( if a r Problem 5. Let f(T) = 12_ x + 1 on the closed bounded interval [0, 3] (a) Make a list of all the critical values of f(r) that fall inside of the closed bounded domain. (b) Evaluate f(r) at the end points of the domain and at all the numbers from part (a) (c) Use the list of values from part (b) to find the absolute maximum and the absolute minimum of f(x) on this domain NOquation x2 = 11x - 10 by * - 11 x + 10 = 0 1x- 10 x+ 10 ( x - jig X x - x) X - 11 x+10 X = 19 * = 1 2. Solve the - 6 x - 2:3,2 6x - 2 = 312 using the qua ons using any method (if Problem 6. Show that the function f(x) = sin () satisfies the Rolle's theorem on the interval [7, "], then find all values of c which satisfy the theorem. Problem 7. Consider the function f(x) = xle z (a) Use a sign chart to find the intervals of increase/decrease for f(). (b) Find the relative maximums and minimums for f(). (c) Use a sign chart to find the intervals of concave up/down for f(z). (d) Find any points of inflection that exist. 31x710*+ 10 11x - 10 by fac X - 11 x +10 * - 11 x + 10FO ( x - 1 18/ X x - V) X = 10 X = 1 6 x - 2 : 3x2 2. Solve the equation 6r - 2 = 312 using the quad Problem 8. Find each of the following limits. 1 - 3x + 5x2 ing any method 1. lim I- 100 1 - 2.12 In r 2. lim 3. lim r tan (1/x) I - + 00 Problem 9. The graph of f'(x) is below. Use this graph to determine the intervals of increase/decrease/ concave up/concave down for f(r). At which r coordinates does f(x) have a local min, local max, or inflection point?X = 10 X = 1 6 x - 2:3 x2 2. Solve the - 2 = 312 using the Problem 10. Consider the function y = Vi2 + r - r using any metho 1. Find all intervals of increase and decrease. 2. Find all relative max/min 3. Find all intervals of concave up and down 4. Find all points of inflection 5. Now graph the function on the axes below labeling all the points you found. 4-3 21 12 3 5