The slope of the line tangent to the curve y = f (x) at the point P (a, f(a)) is given by mtan = lim- x+a f (x) - f (a) -, if the limit exists. X - a 5. (12 pts) Let £ (x) and a = 5. (a) Using the definition above, find the slope, mtan of the line tangent to the graph off at P (a, f (a)). (b) Find an equation of the tangent line in part (a).

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Trinidad TremblayLv2

29 Aug 2018

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3. (15 pts) (I) The graph of the functions (t) =- - t +1 is given below. s=s(t) (a) In the figure above draw a secant line joining the points (o, s (0)) and (2, s (2)). (b) Find the slope, msec, of this secant line. (c) Draw a tangent line to the curve s = s(t) at the point where t = 2. (d) Is the slope of this tangent line, mtan, positive or negative ? 12 - is the position of an object moving along a line (II) Suppose s (t) = — at time to. (a) How is the average velocity, Vav, between the times t = 0 and t = 2 related to the slope msec from the part (I b)? (b) Is the instantaneous velocity, Vinst, at t = 2 positive or negative? Explain.

3. (15 pts) (I) The graph of the functions (t) = is given below. s=s(t) (a) In the figure above draw a secant line joining the points (o, s (0)) and (2, s (2)). (b) Find the slope, msec, of this secant line. (c) Draw a tangent line to the curve s = s(t) at the point where t = 2. (d) Is the slope of this tangent line, mtan, positive or negative ? 12 (II) Suppose s (t) = is the position of an object moving along a line t + 1 at time t 20. (a) How is the average velocity, Vav, between the times t = 0 and t = 2 related to the slope msec from the part (I b)? at t = 2 (b) Is the instantaneous velocity, Vinst positive or negative? Explain.

Problem 2 Let f(x) = 3.72 - 4x + 5 a) (12 pts) Use the definition of the derivative to compute f'(2). Recall that f'(a) = lima f(a+h)-f(a). olt ; alternatively f'(a) = lim f() - f(a) 0 Ir-a b) (8 pts) Find the equation of the tangent line to the graph off at a = 2.

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