Struggling with Calculating Rates of Change in Graphs?

[xX-Cyanide-Xx]

Hey everyone, I am trying to study some questions from the internet and i came across this one. i think this will help me heeps with my study but i just can't figure it out. can anyone els?

......The picture of the graph is in the attachment......


Using the graph above, find:

a) The average rate of change from x = 2 to x = 4
b) The instantaneous rate of change of this function at x = -3
c) The above function is given by y = (x=3)(x - 1)(x - 4). Using your graphics calculator:
I. What is the instantaneous rate of change at x = -2
II. Sketch your screen for how you got this solution.
III. Write down your View Window settings.

 

[Mentallic]

I can help you with the maths part of this problem, but not the calculator side of it. I can't see the attachment yet but it's not a problem.

The average rate of change is given by the slope of the line between the points $$(2,f(2))$$ and $$(4,f(4))$$.
The instantaneous rate of change is given by the tangent at the point $$(3,f(3))$$.

 

[xX-Cyanide-Xx]

So they're both determind by the gradient. Are they?

 

[Mentallic]

Yes that's right.

 

[xX-Cyanide-Xx]

yay. so i just need to find out how to use the graphics calculator to do the rest. but how will i do that?

 

[Mentallic]

I don't see why you would even need to do those questions. You are studying on the net and if you're learning this for school, I doubt they will ever ask you to grab your graphics calculator and answer it in this way. So why even bother?

 

[xX-Cyanide-Xx]

i guess its just so I am prepared, if i can learn the hard stuff, i should be able to do everything they throw at me. andwho knows wat they might give us.

 

[Mentallic]

This calculator business is hard stuff in its own way, not in the way a maths test works. If your school is anything like most other high schools out there, they won't be asking about how to use your graphics calculator.

Unless... you do that regularly in class?

Oh by the way, you need polishing up on those other skills before you should even be thinking of trying to learn about calculators. Calculators seriously aren't helping you at all, you need to become a little more independent with your maths.

But if you're still intent on doing those questions, maybe someone else can help you because I can't.

 

[xX-Cyanide-Xx]

Well, we have been using the graphics calculators a lot in class, so the test does involve them.

but thanks for the help I've learned heeps...:)