Find the average rate of change of the function: f(x)=0.5x-x^2 from x=-2 to x=4

Question

anonymous · Answer

so the y's or the f(x)'s are equal to the x's?

anonymous · Answer

was just trying to figure out how to plug it in correctly, I remembered the formula.  But didn't recall how to get the f(x)'s.

lalaly · Answer

$$f(4)=0.5(4)-4^2$$

anonymous · Answer

nice thanks.  so now I figure the equation using the outcome right?

anonymous · Answer

f(4) = -14

anonymous · Answer

doesn't "rate" mean to differentiate? i think you need to find dy/dx and then put in the value at those points. No?

anonymous · Answer

so I would input -14 in to the $$f(x _{2}) = -14$$

So

$$\frac{-14-3}{4--2}$$

so the average rate of change is:

$$\frac{-17}{6}$$

anonymous · Answer

Is that correct or no?

anonymous · Answer

Can't be right suppose to equal -3/2  but I can't figure out how to get that answer.

anonymous · Answer

dy/dx= 0.5-2x, nowput x= -2 and x= 4, to get gradient which is 4.5 and 7.5, take its average i.e 12/2 = 6

anonymous · Answer

aroc or average rate of change = slope which is y2-y1/x2-x1 which will give your your average rate of change.

anonymous · Answer

which in turn = f(x2)-f(x1)/x2-x1

anonymous · Answer

oh okay