find slope of tangent line y=f(x)=xsquared + 1 at (2,5) given f'(x)=2x

- anonymous

find slope of tangent line y=f(x)=xsquared + 1 at (2,5) given f'(x)=2x

- schrodinger

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- cwrw238

the slope = 2x
at (2,5) x = 2 so slope of tangent = 2(2) = 4

- 2bornot2b

So your question is to find the slope of the equation\(f(x)=x^2+1\) at (2,5) given f'(x)=2x

- 2bornot2b

joycelefebvre are you new to OS?

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- anonymous

yes could you show me your work on that please i'm studying for praxis 0061 my study guied doesnt show work its horrible tu

- 2bornot2b

OK let me help you

- 2bornot2b

Given any function, the derivative of the function is the equation to the slope of the given equation--------did you know that?

- anonymous

kinda I took calc in college in 93 and its not coming back

- 2bornot2b

OK, then I am trying to refresh that.
Suppose you have a function y=f(x), so the function y=f'(x) is the equation of the tangent of the function y=f(x)

- 2bornot2b

OK?

- 2bornot2b

So your given function is \(f(x)=x^2+1\) and \(f'(x)=2x\)

- 2bornot2b

Now as I told you earlier, \(f'(x)\) should be the equation of the tangent at any point

- 2bornot2b

Your question asks you to find the equation of the tangent at (2,5) so just put x=2 in the equation to tangent i.e. 2x2=4.
So the answer is 4
Got it?

- anonymous

omg I was trying to do y2-y1/x2-x1

- 2bornot2b

This is actually a theorem.. If you just remember it you don't have to find the tangent that way.......... I mean the way you are trying using the formula \(\frac {y2-y1}{x2-x1}\)

- 2bornot2b

The theorem is,
Let y=f(x) be a given equation, to find the equation to the tangent at any point is y=f'(x) where f'(x) is the derivative of the function f(x)

- 2bornot2b

Is that clear, any problem?

- anonymous

tu i couldn't find the praxis study guied for 0061 so i got the cliff notes and its all text no examples

- 2bornot2b

Did you know you can chat with other users in the maths group?

- 2bornot2b

In that way you can get help from experts?

- 2bornot2b

Come join me in the chat room (do you know how?)

- anonymous

no

- 2bornot2b

Do you see those green boxes below

- anonymous

your 31

- 2bornot2b

See there I have posted you a chat message

- 2bornot2b

Yes, I am 31, thats my level.

- 2bornot2b

But chatting is a different thing

- anonymous

my lap top keeps telling me i cant run this script

- 2bornot2b

OH, I see, what operating system are you using?

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