(a) At what time is P’s actual acceleration (in ft/sec^2 ) equal to its average acceleration for the
entire race?
(b) What is Q’s acceleration (in ft/sec^2 ) then?
(c) At the end of the race, which auto was ahead? Explain.
- Given that a function f is continuous and differentiable throughout its domain, and that f (5) = 2, f
′(5) = −2, f ′′(5) = −1, and f ′′′(5) = 6.
(a) Write a Taylor polynomial of degree 3 that approximates f around x = 5.
(b) Use your answer to estimate f (5.1).
(c) Let g(x) = f (2x + 5). Write a cubic Maclaurin polynomial approximation for g.
- Let f be the function that contains the point (−1,8) and satisfies the differential equation
(a) Write the equation of the line tangent to f at x = −1.
(b) Using your answer to part (a), estimate f (0).
(c) Using Euler’s method with a step size of 0.5, estimate f (0).
(d) Estimate f (0) using an integral.
