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Math 1151 Midterm 2
Form A
September 27, 2022
1) An object traveling along a horizontal line has displacement function, s(t), graphed below, with s measured in meters and t measured in hours.
a) (5 points) Find the average velocity, vav , of the object during the interval [1, 7]. (Include units.)
b) (5 points) At what time(s) in the interval [1, 7] does the object have instantaneous velocity equal to 0?
c) (3 points) Sketch the line tangent to the graph of s at the point corresponding to t = 1. Label it as T.
d) (3 points) (Write your answer on the space provided.) At which of these times was velocity greatest?
(A) 0.25 (B) 2.75 (C) 3.5 (D) 4 (E) 6.5
2) A function k, with domain (−∞, ∞), has values and derivative values given in the table below.
a) (5 points) Calculate the limit: 
b) (5 points) Calculate 
c) (5 points) Calculate 
3) The entire graph of a function f , with domain (−2, 4), is given below.
a) (3 points) At which point(s) in (−2, 4) is f nondifferentiable?
b) (3 points) Sketch the line secant to the graph of f at the points corresponding to x = 0 and x = 2 on the axes above. Label it as S.
c) (8 points) Sketch the graph of the derivative, f ′ , on the axes below.
4) Let g be the function given by 
a) (6 points) Show that the derivative of g is given by 
(HINT: Use Derivative shortcut formulas.)
b) (4 points) Find a formula for the line tangent to the graph of y = g(x) at the point (4, 2).
c) (5 points) Evaluate the limit: 