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/sci/ - Science & Math

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4353578 No.4353578 [Reply] [Original]

THIS IS NOT A HOMEWORK THREAD.... of sorts

See, we have this pass paper to do, but she said "dont do question 3, as we have not done that work"

but I want to do it anyway, since I wanna learn more so....

The curve C has the equation y = x^2 - 4x + 7. The point A has coordinates (1,4)

a.) Find the equation of the tangent to C at A

b.) Find the equation of the normal to C at the point A

>> No.4353593

a)y=-2x+6
b) y=(1/2)x+6

problem?

>> No.4353598

a) take the derivative of the function at A, find the line that passes through A with slope = that derivative

b) find the line perpendicular to the line in part a that also passes through point A

>> No.4353613

>>4353598
using this, I got

2x +y -6 = 0
2y -x - 7 = 0

right?

>> No.4353614

Take the derivative of C, plug in your x value. That's the slope of the tangent line. Now use point-slope formula
<span class="math">y-y_1=m(x-x_1)[/spoiler]
where <span class="math">y_1,~x_1[/spoiler] are the coordinates of the point you're looking for (in this case, point A).
Normal means perpendicular - it's very simple; once you have the equation of the tangent at point A, just take the negative reciprocal of the slope (and only the slope) and you have the equation to the normal line to point A.

>> No.4353616

i dunno but there is a simple formula of your problem

research it

>> No.4353621

>>4353613
derivate is y'(x) = 2x-4, evaluate this for x=1 and you have the slope of the tangent to C at A.

>> No.4353622

>>4353613
That was Op btw

>> No.4353627

a)y-2+2x=0

>> No.4353634

>>4353614
Why does the negative reciprocal of the slope gives a perpendicular line?

>> No.4353642

Op here again:
Was this right?


2x +y -6 = 0
2y -x - 7 = 0

if its wrong, can you exolain where I got wrong

>> No.4353645

>>4353634

That's just the definition of a perpendicular slope. <span class="math">y=3x[/spoiler] will form a right angle at its point of intersection with <span class="math">y=-\frac{1}{3}x[/spoiler].

>> No.4353658

>>4353642
Curve C is y so why would you put the y on the other side?

>> No.4353664

>>4353593
>>4353613
>>4353642
2x -4 not 2x-6

>> No.4353667

>>4353642

Yes, that is correct. You might want to keep it in <span class="math">y=mx+b[/spoiler] form, to make graphing easier (should you need to graph it).

>> No.4353673

>>4353645
That can't be a definition, I could say it's twice the slope and you would say I'm wrong. What makes a line with slope m perpendicular to a line with slope -1/m?

>> No.4353675

>>4353664
You're wrong.

>> No.4353681

>>4353675
Where is the 6 coming from then?

>> No.4353683

>>4353673

what are you even saying

Are you looking for a proof from me on why the negative reciprocal makes a perpendicular line? I don't do mathematical proofs, I'm a scientist. And even if I knew proof notation, I'm sure you can find one with a quick google search. Don't fucking question me why the math works that way, someone else already figured it out.

>> No.4353689
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4353689

>/sci/
>still doing tenth grade math
>and not understanding it

And you wonder why this board is shit.

>actually, some of you ITT don't even understand seventh grade math

>> No.4354329

>>4353683
lol way to go buddy, you'll go far with this mentality.