Question

Which one of the following does not find the value of f ′(2) for f(x) = x^2 + 3x + 1?
A. f'(2)=lim h->0 ( (2+h)^2 + 3(2+h) + 1 -(2)^2 + 3(2) + 1 )/ h

B. f'(2)=lim h->0 ( (2+h)^2 + 3(2+h) + 1 -[(2)^2 + 3(2) + 1] )/ h

C. f'(2)=lim h->2 (x^2 + 3x + 1 - 11) / (x-2)

Answer 1

or D. all of these find the value for f'(2), but I basically eliminated that one

Answer 2

Could you take a screenshot of the options and attach here ?

Answer 3

Sure

Answer 4

Looks first option and second option are not same. So the false one must be one of them, I guess.

Answer 5

Yeah that's what I was thinking. Would it be the second one?

Answer 6

Nope
http://www-rohan.sdsu.edu/~jmahaffy/courses/s00/math121/lectures/limits_cont_deriv/images/limit2.gif

Answer 7

Wait so is h 0? I've never really understood h

Answer 8

\(h\) is not \(0\)
I can teach you quick if you want to understand

Answer 9

That'd be awesome

Answer 10

Have you visited any other place/city recently ?

Answer 11

which is far away from your home

Answer 12

Yeah, I have

Answer 13

which place ?
starting from your home, how much time did you take to reach that place ?

Answer 14

San Diego, it took about 9 hours

Answer 15

Nice, how far away is it from your home ?

Answer 16

distance...

Answer 17

Oh yes sorry, 2,606 miles

Answer 18

Great! I'm putting everything together in one place :
Home to San Diego in 9 hours
the distance is 2606 miles

Answer 19

let's draw a graph representing this situation

Answer 20

plot time on x axis
and distance travelled on y axis

Answer 21

At time = 0 hours, you were at home and the distance travelled is 0 :

Answer 22

At time = 9 hours, you had reached san diego and the distance travelled is 2606 miles

Answer 23

With me so far ?

Answer 24

Yeah!

Answer 25

Let's also show how you had traveled the distance in between :