Math~Reinyyy

posted by .

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.

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 -

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

Similar Questions

1. Calulus

Consider the following function. f(t) = 3t2 − 3 (a) Find the average rate of change of the function below over the interval [3, 3.1]. (b) Compare this average rate of change with the instantaneous rates of change at the endpoints …
2. Math

Verify if question a is correct I calcuated twice now and I am getting 0 as an answer. I don't understand question b a) Examine the function f9x) =2(0.5x-1)^2(x+2)^2. Determine the function's average of change from -2<x<2. I …
3. Math

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 …
4. Function: Rate of Change

Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the x-axis at 45°. He also determines the instantaneous rate of change at x = 0, π, …
5. function rate of change

Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the x-axis at 45°. He also determines the instantaneous rate of change at x = 0, π, …
6. rate of change

Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the x-axis at 45°. He also determines the instantaneous rate of change at x = 0, π, …
7. Calculus

I have a couple of questions and i wanted to know if my answers are correct. Thanks in advanced! 1. Determine the values of x for which the function f(x)=x+2/x-2 is discontinuous Would the answers be x=2 because the function would …
8. Math

Determine which function has the greater rate of change in this question?
9. Math

The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function …
10. math

Two functions, A and B, are described as follows: Function A y = 9x + 4 Function B The rate of change is 3 and the y-intercept is 4. How much more is the rate of change of function A than the rate of change of function B?

More Similar Questions