trouble w/ derivatives: finding fcn from limit; graphing f'

[sungjin6458]

I need help with the following:

1. The limit represents f'(c) for a function f and a number c. Find f and c.

lim(h->0) [(5 - 3(1 + h)) - 2] / h

I don't know how to start this. I solved the limit out and got -3 but the answer is supposed to be "f(x) = 5 - 3x at c = 1".

2. How do you graph the derivative f' by looking at a graph of f? Can you explain it step by step please?

Thank you!

 

[stapel]

1) Given f(x) and a value c, how do you set up the limit? This question is just asking you to work backwards.

2) Note that f'(x) is the slope of f at x. So look at the graph of f, and estimate the slope at various x-values. Then plot those slope-values as y-values on your graph of f'.

Eliz.

 

[sungjin6458]

help

so how would you work that backwards? please help me again i dont understand how i am supposed to use the given info to get the answer

 

[skeeter]

f'(c) = lim(h->0) [(5 - 3(1 + h)) - 2] / h

f(c+h) = 5 - 3(1 + h)
f(c) = 2

looks like c = 1, and f(x) = 5 - 3x

How do you graph the derivative f' by looking at a graph of f? Can you explain it step by step please?

start by looking at the slope of f ... start by finding those x-values where the slope = 0 ... the graph of f' = 0 at those x-values.

then look between those x-values where the slopes of f is zero ... the slope of f in those regions will be either (+) or (-). the graph of f' will have (+) or (-) y-values in those regions.