MA1M01 Calculus Assignment 7

1. Find the antiderivatives of the following functions:

(a)f(x) = 18x5 − 24x3 − 10x+ 3

(b)g(x) = (1 − π)x−π + 16x−1

(c)h(x) = 30 cosx− 5ex − 7 sinx

(Remember to put in the constants of integration.)

2. A cheetah starts from a standstill (in other words the speed of the cheetah at t = 0 is0) and accelerates according to the following equation:

a(t) = −4t3 + 24t2 − 48t+ 32

for 4 seconds where t is measured in seconds and a(t) is in m/s2.

(a) Find the function v(t) describing the speed of the cheetah over the 4 second interval.

(Hint: The derivative of speed is acceleration so find∫a(t) dt and then find the

constant of integration using the fact that the cheetah starts at a standstill, i.e.v(0) = 0.)

(b) Find the function d(t) describing the total distance the cheetah has travelled fromthe starting point over the 4 second interval.

(Hint: The derivative of distance travelled is speed. Keep in mind the fact thatd(0) = 0.)

(c) How far has the cheetah travelled at t = 4?

3. Let f(x) = e3x5−5x3 on the interval [−2, 2].

(a) What are the critical values of f?

(b) What are the maximum and minimum values of f on this interval?

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