1. Let f"(x) =5- (In2)27. Find an equation for y = f(x) given f has a local minimum of at c = 1.2. Consider the limit: lim _ (20 ) /25 - (-5+ 10:) (a) Express the limit as a definite integral of the form [ f(x) de. (b) Evaluate the definite integral in part (a) by interpreting it as an area of a known shape.3. The graph of the function f is given below: 2 0 4 9 11 12 13 14 t -2 y = f(t) Let F(x) =/ f (t ) dt . (a) Evaluate F(2). (Show all calulations completely by splitting the relevant area into known shapes and labeling them) (Note: the question is NOT asking you to find f (2)).(b) Determine a formula for F'(x) using a theorem from class. Fully justify your answer. (Your final answer may have f terms). (c) Evaluate F' (1)