Question

use the lim f(x)-f(a)/(x-a) to find the derivative of 5x^2 - 3x + 2, a =1
x->a

Answer 1

the derivative equation is

\[\lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}\]

try using that instead of wahtever you have there

Answer 2

I realize this, but on my quiz we have to know how to use the other one, because we are looking for a specific point. I understand you substitute, but I am having problems with the factoring. I am getting (5x^2 -3x + 23)/(x-1)

Answer 3

It's called the definition of a derivative at a point.

Answer 4

oh i see what an odd equation, but it makes perfect sense

unless you can factor 5x^2...., you're done

Answer 5

Oh. Thought there was more factoring to be done. Thanks.

Answer 6

oh wait hold that thought

Answer 7

ok big issue, you need to find the limit as x->1

this will give you a zero on the bottom

so what you do is you divide all the terms by x and simplify it
then you find the limit

Answer 8

The simplifying is where I'm having the problem. I'm stuck with that fraction and don't know where to go from there.

Answer 9

\[\lim_{x \rightarrow a}\frac{5x^2 -3x + 23}{x-1}\]

Answer 10

actually, no, im completely clueless
a =1 not infinity or 0,
theres not way to get rid of the x-1 in order to find the limit

Answer 11

Exactly. Any ideas? Did I do something wrong to get that fraction?

Answer 12

how did you get 23?
but that doesnt really change anything

Answer 13

plug a = 1 into the function, you get 24. When you write the fraction after substitution like thid
\[\lim_{x \rightarrow 1}\frac{ 5x ^{2}-3x+24-1 }{ x-1 }\]

Answer 14

24-1=23

Answer 15

the formula says f(x)-f(a), so that is why it is -1

Answer 16

\[\lim_{x \rightarrow a} \frac{5x^2 - 3x + 2-(5a^2 - 3a + 2)}{x-a}\]
\[\lim_{x \rightarrow a} \frac{5(x^2-a^2) - 3(x-a)}{x-a}\]
\[\lim_{x \rightarrow a} \frac{5(x-a)(x+a) - 3(x-a)}{x-a}\]
\[\lim_{x \rightarrow a} \frac{(x-a)(5(x+a) - 3)}{x-a}\]
\[\lim_{x \rightarrow a} 5(x+a) - 3\]
\[5(a+a)-3\]

a=1
7

Answer 17

substitution always comes last
my mistake

Answer 18

and this is why i cant be lazy and rely off other people's work :(

Answer 19

This looks likes the same process as the other formula. Is it essentially?

Answer 20

it is the same thing, sort of
basically you need to understand the slope equation

Answer 21

[f(x+h)-f(x)]/(x+h-x)

in this case, x+h=x and x is equal to a

Answer 22

Okay, thanks for your help.