Posted by Elli on Monday, December 19, 2011 at 9:14pm.
Could someone help me with these questions, I don't know question c) and d)
Consider the function f(x) = (0.1x1)(x+2)^2.
a) Determine the function's average rate of change on 2<x<6.
Answer; Avg rate of change is 3.2
b) Estimate the instantaneous rate of change at x=2.
Answer 4.7999
c) Explain why the rates of change in parts a) and b) have been negative
d) Give an interval on which the rate of change will be increasing?

Math  Steve, Tuesday, December 20, 2011 at 4:40am
f(x) = .1(x10)(x+2)^2
So, it has a double root at x = 2 and another root at x = 10.
Since it's a cubic, with positive coefficient for x^3, it rises from the left, brushes against the xaxis at x = 2, decreases and comes back to cross again at x=10.
f is decreasing at the places of interest.
Any interval where x > 10 will have f increasing. Since you ask about instantaneous changes, I assume you know about derivatives.
f' = .1 ( 3x^2  12x  36 )
f' = 0 at x = 2 and 6
So, f is increasing for x < 2 and x > 6