I I z 1) Let F(x)=I:1:(t2)dt. Find the exact values of F(0), F'(0) and F\"(0). Explain. O 2) The graph of the function y = f (x) is shown below. Use the facts that F ' = f and F(0) =1 to answer the following questions. a) Complete a table of values for y = F(x) for integer values of x from 3 to 5. b) Where does F have critical points? 0) Sketch an accurate graph of F, clearly showing the concavity of the graph. (1) Find the global maximum and global minimum values of F on the interval [3,5]. Next page 2 3) The function defined by S(x) = sin |dt is called the Fresnel sine function (after the French physicist Augustin Fresnel) and is used in the study of optics. a) Find a [s(x)]. b) Use calculus to find the exact location (x-values) of all relative extrema of S (x) in the interval [0, 2.5] and classify them as relative maxima or relative minima. (Be sure to include a sign chart.) c) Graph S(x) in Desmos (type "int" to create integral), using a viewing window of [-3,3] by [-1, 1] and confirm your work in part b). Upload the graph with your work (or include a link to it in the comment section)