Question

Could someone help me with these questions, I don't know question c) and d)

Consider the function f(x) = (0.1x-1)(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?

Answer 1

f(x) = .1(x-10)(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 x-axis 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