Differentiation Help!

Original post by DenizS

What is the information in the question trying to tell you? :h:

Reply 2

so first we differentiate

dy/dx = 12x + 2

then whenever you want to find the gradient at a point of x of a curve, sub it in

tangent gradient formula:
-1/gradient of curve

any questions?

Reply 3

Original post by frankielogue

so first we differentiate

dy/dx = 12x + 2

then whenever you want to find the gradient at a point of x of a curve, sub it in

tangent gradient formula:
-1/gradient of curve

any questions?

If you differentiate, wouldn't it be 8x+2?

Reply 4

Original post by SeanFM

What is the information in the question trying to tell you? :h:

That one line is parallel and the tangent is parallel to the point.

Reply 5

RogerOxon

Original post by DenizS

Differentiate the curve's equation and set that equal to the gradient of the line to obtain the x co-ordinate of the point on the curve with the same gradient.

Use that x coordinate to find the y coordinate on the curve, then calculate the equation of the line (using the point and the gradient).

Reply 6

Original post by DenizS

That one line is parallel and the tangent is parallel to the point.

So when two lines are parallel..

Reply 7

Original post by SeanFM

So when two lines are parallel..

they have the same gradient, so is my gradient 2?

Reply 8

Original post by DenizS

they have the same gradient, so is my gradient 2?

Correct, now how can you use this information?

Hint: to find the equation of the tangent you need one set of co-ordinates and the gradient.. you have the gradient and somehow need to find the x,y co-ordinates by using that the gradient is 2.

Reply 9

Original post by SeanFM

Do I substitute?

Reply 10

Original post by DenizS

Do I substitute?

Substitute what? Why? How? Try stuff and see if it makes sense and if it works :smile:

Reply 11

Original post by DenizS

If you differentiate, wouldn't it be 8x+2?

**** you’re right
sorry i’m brain dead today

Reply 12

Original post by SeanFM

Substitute what? Why? How? Try stuff and see if it makes sense and if it works :smile:

Okay so I have y=2x+3. If I differentiate that I get y=2x

Then if I differentiate y=4x^2+2x+6, it's y=8x+2

My gradient is 2

So my equation is something along the lines of y=2x+c (?)

Reply 13

Original post by DenizS

Okay so I have y=2x+3. If I differentiate that I get y=2x

Then if I differentiate y=4x^2+2x+6, it's y=8x+2

My gradient is 2

So my equation is something along the lines of y=2x+c (?)

Harmless but also wrong direction to differentiate y = 2x +3.

Let's go over the information again:

The line y=2x+3 is parallel to the tangent of a curve at a point. The equation of the curve is y=4x^2+2x+6. What is the equation of the tangent?

Let's call 'the point' (x,y). Now, we already know that at (x,y), where y = 4x^2 + 2x + 6, has the gradient 2 because y = 2x+3 is parallel to the tangent at that point.

So you know that at some point on the curve y = 4x^2 + 2x + 6, the gradient is 2.

Do you understand how we got there and what to do next?

Reply 14

Original post by SeanFM

The only thing I can think of is y-y1=2(x-x1)

Reply 15

but otherwise, it still stands, so if you wanted to find the tangent of the curve at say x = 2, sub it in:

8x + 2
= 16 + 2 = 18

then we write it in the form y - y1 = m(x - x1)
= y - 26 = 18(x - 2)
and we rearrange to get y = 18x - 10

we get the 26 y value because when we sub x as 2 into the original, we get 26

also disregard my aforementioned formula of -1 / gradient, that’s for the normal. i’m so brain dead.

Reply 16

Original post by DenizS

The only thing I can think of is y-y1=2(x-x1)

Correct, we do need to use that, just as soon as we find out what x1 and y1 are, which is the step inbetween.

Read over my previous post again and think about how to use the fact that you know the gradient is 2 at the point (x1,y1) on the line y = 4x^2 + 2x + 6.

Hint: you were correct in differentiating y = 4x^2 + 2x + 6

Reply 17

that’s my take on it anyways

Reply 18

Original post by SeanFM

If I solve the equation for 4x^2+2x+6, will that help?

Reply 19