Question

How to find the slope of the curve f(x) = x^3 - 2 at x=1?

I got m=1 but the answer is m=3. How do you get m=3?

My work:

m=(1+h)^3 - 2(1+h) - ((1)^3 - 2) / h

=

(h^3 + 3h^2 + 3h +1) - (2+2h) - (-1) / h

=

(h^3+3h^2+h) / h

=

h(h^2+3h+1) / h

= (h^2+3h+1) = 1

Answer 1

By taking derivative of it, gives you the \(\text{Slope}\) of the curve.. :)

Answer 2

Derivative of Curve I mean.. :)

Answer 3

Oh, I did not see that you have changed the question.. :P

Answer 4

So, you have : \(f(x) = x^3 - 2\)

Answer 5

Have you found its derivative?

Answer 6

you can type your work here in the comments, I am looking down here to find your replies, and you are giving it in the question itself everytime.. :P

Answer 7

I'm sorry, first time using website lol.

Answer 8

I know, see just type your question above, and you can type your answer there too, but final answer.. Steps and discussion, we will do here in comments.. Okay?

Answer 9

Now, don't change your question, I am seeing your steps.. :)

Answer 10

Thank you so much! :)

Answer 11

See, there is no \(x\) with \(2\), right??

Answer 12

Oh..
So it doesn't require the input

Answer 13

yes, you should not multiply \((1+h)\) with \(2\), try without it..

Answer 14

\[m=\frac{((1+h)^3 - 2) - ((1)^3 - 2)}{ h}\]

Answer 15

See, you replace \(x\) by \((1+h)\), right?? so replace it, only where you are seeing \(x\)..

Answer 16

Getting?

Answer 17

Yes, I understand

Answer 18

Are you getting \(3\) now?

Answer 19

No

Answer 20

Really?

Answer 21

Wait..
I think I found my mistake

Answer 22

Oh, go slow, the advantage is, you will commit less mistakes.. :) Don't worry, we learn from our mistakes only.. :)

Answer 23

I got the answer!!
:D

Answer 24

:)

Answer 25

Thank you!

Answer 26

\[\huge \color{green}{\textsf{Welcome To Openstudy...}}\]

Answer 27

Could you help me with another problem?

Answer 28

you are welcome dear.. :)

Answer 29

yeah sure..

Answer 30

If you're not busy ;p

Answer 31

Don't worry, if in case I am busy, then also you will keep getting help here, I assure you.. We also want to help those who are serious and come here for studying.. I found you serious as you showed your steps, told your answer, this means you have really tried this problem and unfortunately, you got some doubt, for which you are here.. :)

Answer 32

I'm not sure if I'm suppose to multiply by the conjugate =/

Answer 33

What is the question statement?

Answer 34

\[f(x) = \sqrt{x-6}\]

Answer 35

at x=14

Answer 36

Whole statement??

Like your question what I think is : Find the value of \(f(x) = \sqrt{x-6}\) at \(x=14\) ?? Right?

Answer 37

Correct

Answer 38

Okay, are you seeing \(x\) there?? you are just replace that \(x\) with \(14\) as you are given \(x = 14\)..

Answer 39

Oh dear, Electricity has gone, UPS is going to kill me and my pc now.

@mayankdevnani please help here.. :)

Answer 40

@mayankdevnani help here.. :)

Answer 41

I did:

m=\[\sqrt{14+h-6} - \sqrt{14-6}\] = \[\sqrt{h+8} - \sqrt{8} \]

Answer 42

All divided by h

Answer 43

yeah !!! i am just reading the question

Answer 44

wait !!!

Answer 45

is this your question ? @thisissammy

Answer 46

Yes

Answer 47

just plug the value of x=14 in the equation

Answer 48

and then simplify the equation!!

Answer 49

*Find the slope of the curve

Answer 50

oh!!!

Answer 51

@thisissammy
follow these steps :-

Answer 52

http://www.seriesmathstudy.com/tangentexample.htm
please go through this site,this site must help you :)

@thisissammy

Answer 53

@thisissammy first,find out the derivative of the given function

Answer 54

@waterineyes i do my best :)

Answer 55

are you there ? @thisissammy

Answer 56

http://www.seriesmathstudy.com/tangentexample.htm
please go through this !!

Answer 57

how to find derivative :-
1) http://www.mathsisfun.com/calculus/derivatives-introduction.html
2) http://www.youtube.com/watch?v=vzDYOHETFlo
3) http://www.youtube.com/watch?v=54KiyZy145Y
4) http://www.youtube.com/watch?v=WERgBgi4hg4
5) http://www.youtube.com/watch?v=ydHzk5zWd4I
and the most important :-
6) http://www.youtube.com/watch?v=HtGCDWsYAVY

Answer 58

first go through this ^^^^^^^^^^^^^^^^^

Answer 59

Thank you for the sources

Answer 60

welcome :)
i hope now you can find out derivative of any function

Answer 61

if not,then please take your time to learn and i hope now you can solve your question yourself :)

Answer 62

Have you been taught the normal method for finding derivative? Or you have just learned finding the derivative using Fundamental Definition??

Answer 63

I mean, I have seen you found the derivative using fundamental definition : using (1+h) and h all that..

Answer 64

Other method is :
\[\frac{d}{dx} x^n = n \cdot x^{n-1}\], although it is proved from fundamental definition.

Answer 65

So: \(f(x) = x^3 - 2\), \(f'(x) = 3x^2 - 0\), derivative of constant is \(0\), so derivative of (-2) is \(0\)..

Answer 66

So, \(f'(x) = 3x^2\), now put \(x= 1\), \(f'(1) = 3 = m\).. :)

Answer 67

Getting ?

Answer 68

That is what I was thinking that you asked first question on finding the slope of curve, then how could second question be so simple having just a value to plug in it.. :P

Answer 69

So, I saw that you have reached to:

\[m= \frac{\sqrt{h+8} - \sqrt{8}}{h}\]

Answer 70

Right?

Answer 71

Of course with limit \(h\) tends to \(0\)..

Answer 72

I haven't been taught the normal way yet

Answer 73

But that is what I reached ^

Answer 74

I am yet on that place only.. :P

Answer 75

I have not used fundamental definition for derivatives, so I am not very good at it, I can do it other way, but you are yet to reach there.. Don't worry, if we will solve, then we will solve this only, no other way.. :)