Consider a function f that is differentiable at a point a: = a. The tangent line to the graph of f at a is given by the equation 9 = u) + f'(a)($ - [1) Draw a diagram illustrating equation for the tangent line. You may briey describe why your diagram illustrates the equation. Let f be continuous over the closed interval [0,, b] and differentiable over the open interval (55,5). The mean value theorem states that there exists at least one point c such that a 00 k=1 provided the limit exists. Here at is any point in the subinterval [Xx-1, Xx]. (We typically have considered when a* = Ck-1 or a* = xx for left and right Riemman sums, respectively.) Draw a digram illustrating the limit definition of the definite integral. You may briefly describe why your diagram illustrates the definition.Let f(a:) be continuous over an interval [(1, b]. The mean value theorem for integrals states that there is at least on point e such that a S C S b and b h ab/ mass or / f(w)dx=f(c)