Question

Find f '(x). f(x) =2x^2 ; a=1.
Has to be with f(x+h)-f(x)/h formula.
Show steps please.

Answer 1

1. expand 2(x+h)^2

Answer 2

what do you get?

Answer 3

2x^2+4xh+2h^2

Answer 4

subtract 2x^2 from that

Answer 5

{ f(x+h) -f(x) } done!

Answer 6

(2h^2 +4xh)/h

Answer 7

common term?

Answer 8

h

Answer 9

2h

Answer 10

'cancel' it

Answer 11

2h+4x

Answer 12

\[\lim_{h \rightarrow 0} (2h+4x) = ..?\]

Answer 13

4x

Answer 14

done:)

Answer 15

I love you

Answer 16

I love you too.

Answer 17

I'm gonna try the next one by myself :D

Answer 18

Can you answer this? Why is the derivative important?

Answer 19

It's change. Change is important and sometimes positive.

Answer 20

Even if it's negative, still good to understand it.

Answer 21

But couldn't we just find a point close to our original? Seem like the lim and secant line are unnecessary.

Answer 22

Sure, but 4x is general, it works anywhere... why bother doing calculations for each point when you could just use something that works for every point.

Answer 23

Right. Well ,I forgot there was a second part to the problem, which is: find the tangent line to the graph of y=f(x) at x=a

Answer 24

you found the slope of any tangent line at any x (4x)...
at x=a =1 the slope of the tangent line is 4*1
a point which the tangent line goes through is (1 , 2(1)^2)
so now you know a point on the line and the slope of the line..
can you find the equation for the line?

Answer 25

omg it is so easy!

Answer 26

Why didn't I see that?

Answer 27

:)

Answer 28

:(

Answer 29

So let me see if I can figure the line out.

Answer 30

I'm not getting the right equation. The answer in my book is y=4x-2

Answer 31

yes

Answer 32

2 = 4*1 +b
b=-2

Answer 33

I got y=4x

Answer 34

y=4x -2

Answer 35

y-4=4(x-1)

Answer 36

y-2 =4(x-1)

Answer 37

point on the tangent line is the point on the original function where the tangent line 'hits' it = (1, 2*(1)^2) = (1,2)

Answer 38

Whoops, I plugged the given number into f '(x) instead of f(x)

Answer 39

so if a=2 my point would be 2,8, right?

Answer 40

yep:)

Answer 41

Okay, just making sure. Thanks for the help!

Answer 42

sure!