1. ## calculus

I seen a question on a practice paper a while back which confused me a 'lil. Here it is:
Source: [6663]Edexcel GCE Core Mathematics C1 AS - Monday 10th Januaryy 2005

Question 9

The gradient of the curve C is given by
$\frac{dy}{dx}
=(3x-1)^2$

The point P(1,4) lies on C. (For reference, but was used for questions A and B)

c) Using dy/dx, show that there is no point on C at which the tangent is parallel to the line
$y=1-2x$

I don't know where to start on this question, so any help would be great :x, especially since I have a C1 exam in ~ 2 hours. D:

So far, all I know is that the gradient of $y=1-2x$ is obviously -2 and the increment (+1) doesn't matter (hence, parallel).
$(3x-1)^2=9x^2-6x+1$
So those are the 2 gradients of the equasion, and I have no idea on how to show that there's no point on C where they're parallel.

I seen a question on a practice paper a while back which confused me a 'lil. Here it is:
Source: [6663]Edexcel GCE Core Mathematics C1 AS - Monday 10th Januaryy 2005

Question 9

The gradient of the curve C is given by
$\frac{dy}{dx}
=(3x-1)^2$

The point P(1,4) lies on C. (For reference, but was used for questions A and B)

c) Using dy/dx, show that there is no point on C at which the tangent is parallel to the line
$y=1-2x$

I don't know where to start on this question, so any help would be great :x, especially since I have a C1 exam in ~ 2 hours. D:

So far, all I know is that the gradient of $y=1-2x$ is obviously -2 and the increment (+1) doesn't matter (hence, parallel).
$(3x-1)^2=9x^2-6x+1$
So those are the 2 gradients of the equasion, and I have no idea on how to show that there's no point on C where they're parallel.
parallel means they have the same slope. so you need to show that dy/dx = -2 is never true.

this should be somewhat obvious. dy/dx is a square, and is thus greater than or equal to zero for all x, while -2 < 0. they cannot be equal

thus, dy/dx never matches the slope of the line in question and so there is no tangent line that is parallel to the said line