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# Limits and Derivatives watch

6. Compute f'(a) in two ways, using Eq. 1 and 2.

Eq. 1:

Eq. 2:

Where,

.

8. Refer to f(x) in figure 11 when answering this question.

Compute . What does this quantity represent?

This quantity represents the average rate of change of y with respect to x over the interval [1, 2.5] (or the average rate of change of function f over the interval [1, 2.5]).

22. First find the slope and then an equation of the tangent line to the graph of at x=4 using the definition of a derivative.

Slope of tangent = 1/4.

Point on tangent: (4, 2)

Would I have to consider the tangent to the curve at (4, -2) as well?

Equation of tangent:

God, limits latex is a pain in the butt.

Thanks again!
2. They all seem right to me.

For Q22, you don't need to consider (4,-2) since refers only to the positive square root (otherwise it wouldn't be a function).
3. Using the limit definition, compute f'(x)

I'm having problems with the algebra.
4. (Original post by Doughboy)
Using the limit definition, compute f'(x)

I'm having problems with the algebra.
Using method 1 from your first post, once you've sorted the fractions in the numerator so everything is over a common denominator, what can you multiply top and bottom by to get rid of the square roots on top?

Spoiler:
Show

You want to get to the form in the numerator.

If you're still stuck, post where you've got to.
5. Hey, sorry but I figured out how to solve the problem.

I think I ended up with a term including

I was having a hard time getting it to because I was overlooking the simple laws of indices.

Thanks
6. (Original post by Doughboy)

6. Compute f'(a) in two ways, using Eq. 1 and 2.

Eq. 1:

Eq. 2:

Where,

.
I'd possibly add another step in the last line for clarity: (as you have been very detailed so far in your working) But it shouldn't cost you any marks as written.

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Updated: October 4, 2010
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