Two hours after the start of a 100-kilometer bicycle race, a cyclist passes the

Question

Two hours after the start of a 100-kilometer bicycle race, a cyclist passes the 74-kilometer mark while riding at a velocity of 40 kilometers per hour. Complete parts (A) through (C) below (A) Find the cyclist's average velocity during the first two hours of the race. kilometers per hour (B) Let f(x) represent the distance traveled (in kilometers) from the start of the race (x 0) to time x (in hours). Find the slope of the secant line through the points (O,f(O) and (2,f(2)) on the graph of y f(x) kilometers per hour (C) Find the equation of the tangent line to the graph of y f(x) at the point (2,f(2)) Type an equation).

Explanation / Answer

Average velocity = total distance / total time = 74 / 2 = 37 kms per hour

b) Slope of the secant line between ( 0, f(0) ) and (2, f(2) ) = f(2)-f(0) / 2-0 = 74-0 / 2-0 = 37

c) At the point (2,f(2)) velocity = slope of distance vs time graph = 40 kmph
Equation of tangent in point slope form =
y-y1 = m (x-x1)
y-74 = 40 (x-2)
y= 40x + 74 -80
y= 40x - 6

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