Differentiation Qs - Please help!!!!

[ggxxx]

Hey all!
I've been preparing for a SAC I have in a couple of days by doing heaps of questions and there is a fair few I'm stuck on... (I'm pretty fair at maths :S). I thought I'd post some here and maybe someone could help me in them. Doesn't have to be all, but even a few Id be grateful
Thanks so so much!

1   The average rate of change of the function y = 2 x 3^x over the interval [0, 4] is:
A   40.5
B   162
C   158
D   40
E   4

Given f(x) = x^3 - 2x, the average rate of change of f(x) with respect to x for the interval
[-2, 0] is:
A   -2
B   2
C   5
D   -3
E   6

(I don't get rates of change!)

The gradient of the chord of the curve y = 2x^2 between the points where x = 1 and
x = 1 + h is given by:
A   2(x + h)^2 - 2x^2
B   4x + 2h
C   4
D   2h
E   4 +2h


7   A golf ball is hit so that its height h(t) metres above the ground t seconds after it is hit is given by h(t) = 3t(8 t). The maximum height reached is:
A   48 metres
B   24 metres
C   8 metres
E   10 metres
E   14 metres


12   The graph of y = | x^2 - 4 | is differentiable for:
A   x E R
B   x E R+
C   x E [-inf, 0]
D   R\{-2, 2}
E   [-2, 2]


PLEASE HELP!

[taiga]

I don't think I'll do all of them for you, but to start you off

1   The average rate of change of the function y = 2 x 3^x over the interval [0, 4] is:
A   40.5
B   162
C   158
D   40
E   4

sub in x= 0 and x=4 and record the y values
x=0, y= 2
x=4, y= 162
Rate of change = change in y/change in x = 160/4 = 40
Hence D

---

The gradient of the chord of the curve y = 2x^2 between the points where x = 1 and
x = 1 + h is given by:
A   2(x + h)^2 - 2x^2
B   4x + 2h
C   4
D   2h
E   4 +2h

So gradient = rise/run = change in y / change in x

So if we go from x = 1 to x = 1 +h, that means we went up by h, hence the change in x is h.
When x = 1 , y= 2
When x = 1+h, find what y equals, and then write down that value.

Your answer will be  = (Final Y Value - 2)/h

[luken93]

1:
Average Rate of Change =

[ggxxx]

Thanks! Now I think I remember rates of change - I did that last year
Thanks heaps! If you don't mind just one more - i have no idea how to do 7 :S the ball one...

[Russ]

For 7:

Recognize that the maximum height will be the turning point of the graph (where the gradient = 0)
Not sure what the weird symbol is but you need to differentiate then set equal to 0 and solve. If you can't differentiate it, post the actual equation and I'll show you

[pi]

12   The graph of y = | x^2 - 4 | is differentiable for:
A   x E R
B   x E R+
C   x E [-inf, 0]
D   R\{-2, 2}
E   [-2, 2]

D, those two points are cusps

[Water]

Though this comment isn't helpful, thats one wierd looking symbol there.

[ggxxx]

Wow thank you so much to everybody!
The symbol was simply meant to be a "-"... strange
Thanks again!

[panicatthelunchbar]

For question 12, note that you cannot differentiate a modulus function.
So, the easiest method is drawing the graph of the function and then describing it using a hybrid function.
You can then differentiate the hybrid function.

[pi]

For question 12, note that you cannot differentiate a modulus function.
So, the easiest method is drawing the graph of the function and then describing it using a hybrid function.
You can then differentiate the hybrid function.

Um, you can. Using the signum functions (although technically, the signum function is also a hybrid function to0). But for that question, you didn't need it.

[panicatthelunchbar]

What's the signum function?

[pi]

What's the signum function?

Don't worry, you don't need to know.

http://en.wikipedia.org/wiki/Sign_function