différenciation

[waxen burrow]

Can someone help with this thanks. <@&791435371564892232>

[faint smelt]

So first we need to find the gradient of the tangent to the line

we can do this by differentiation, the way i knew it is for each term that has x, you apply the formula x^n = nx^n-1

so our derivative is 2+1/x^2
then substitute x = 1 and you should get 3 which is the gradient of the tangent

now we still need one coordinate, since they're talking about at x=1, substitute this into the original equation y = 2x - 1/x, and the y value should be 1 so the coordinate is 1,1

Now that we know the tanget has a gradient of 3 that goes through 1,1 we can use y-y1=m[x-x1] to find the equation
y-1=3[x-1]
y=3x-3+1
y=3x-2
from there you can find the values for a and b

[waxen burrow]

Thank you so much ! I understand 👍🏻

[faint smelt]

no problem c:

[waxen burrow]

Bc Initially I thought the gradient would be 2

[faint smelt]

i haven't acc done this topic yet for alevel i just knew this from further maths

[waxen burrow]

Woah that's cool

[faint smelt]

yea cause 1 keeps coming up here everywhere so it looks confusing

[faint smelt]

yeah i was gonna study it but then i got a new teacher and they just cancelled it, i still had my textbook so i just read it to prepare for sixth form

[waxen burrow]

I mean like bc on the question it said
The tangent to the curve is
Y = 2x - 1/x

Like isn't that the equation for the tangent

So would it not be 2 ?

[waxen burrow]

Woah u understand textbook

[faint smelt]

because the equation is not linear, so if you drew out this equation

[waxen burrow]

Ohhh

[faint smelt]

it would be curved and so it could be very steep and very sloped at times

[waxen burrow]

That makes so much sense

But how could that be still called a tangent

[faint smelt]

the tangent line touches the curve at a specific point

so like if u remember from circle theorems how a tangent touches the circle

its basically that with the curve y = 2x - 1/x

[waxen burrow]

Ohhh right

Makes sense

Thxx