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I'm working on a calculus multi-part question and need support to help me learn.
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1. Suppose the position equation for a moving object is S(t) = -4tº +8t, where S is measured in decameters
and t is measured in microseconds.
a) What is the average velocity of the object from 1 to 2 microseconds? include units in the answer.
b) What is the instantaneous velocity of the object at t=2 microseconds? include units in the answer.
c) What is the acceleration of the object at t=2 microseconds? include units in the answer.
d) Find the velocity of the object when it hits the ground. include units in the answer.
e) Find the maximum height of the object.
1
at the point (-4,-3).
2. Find the equation of the line tangent to y =
x-2
x + 6
Provide your answer in slope intercept form.
3. You are given the following information.
f(0) = 5
f'(0) = 3 f(2) - 1 f'(2) = 5
g(0) = 2 g'(0) = 4 8(2) = 0 g' (2) - 4
Use this information to find each of these derivatives. Show all calculations.
a) (fºg)'(2) -
b) If k(x) = f(cosx), find k'
이
4. Find the 54th derivative of the function f(x) = 2 - 4 sin(2x). You must show all supporting work for full
credit.
2
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