(a)
(b)
(c)
(a)
(b)
(c)
(a)
(b)
(c)
(d)
At what time is P’s actual acceleration (in ft/sec^2 ) equal to its
average acceleration for the entire race?
What is Q’s acceleration (in ft/sec^2 ) then?
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.
Write a Taylor polynomial of degree 3 that approximates f around x
= 5.
Use your answer to estimate f(5.1).
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
Write the equation of the line tangent to f at x = −1.
Using your answer to part (a), estimate f(0).
Using Euler’s method with a step size of 0.5, estimate f(0).
Estimate f(0) using an integral.
