Posted by **Elli** on Tuesday, December 20, 2011 at 12:18am.

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?

- Math~Reinyyy -
**Damon**, Tuesday, December 20, 2011 at 4:32am
If the function is decreasing, the rate of change is negative.

The cubic function is zero at x = -2 and at x = 10

it is negative for large negative x

It is positive for large positive x

So it slopes down from x = -2 to x = +6

d) derivative = 2(.1x-1)(x+2) + .1(x+2)^2

= 2[ .1 x^2 -.8 x -2] +.1[x^2 + 4 x + 4]

= .2 x^2 - 1.6 x - 4 +.1 x^2 +.4 x + .4

= .3 x^2 - 1.2 x - 3.6

where is that zero?

0 = x^2 - 4 x - 12

0 = (x-6)(x+2)

so the slope of this function is zero at x = -2 and at x = 6

Sketch this function and you will see that the slope is only positive where x is less than -2 and where x is greater than 6

## Answer this Question

## Related Questions

- Math - Could someone help me with these questions, I don't know question c) and ...
- Math - Verify if question a is correct I calcuated twice now and I am getting 0 ...
- Calculus - I have a couple of questions and i wanted to know if my answers are ...
- Calulus - Consider the following function. f(t) = 3t2 − 3 (a) Find the ...
- math - A function is given below. Determine the average rate of change of the ...
- function rate of change - Joe is investigating the rate of change of the ...
- Function: Rate of Change - Joe is investigating the rate of change of the ...
- Math - Determine which function has the greater rate of change in this question...
- math help please - Determine which function has the greater rate of change in ...
- math - Determine which function has the greater rate of change in questions 1&#...

More Related Questions