Maths 2U help- pre calculus

[sayma]

Hi there, could you please help me with this question:
Find the point on the curve y= x^2– x+1 at which the tangent has a gradient of 3.

[Natasha.97]

Hi!

1) Differentiate the equation to find the gradient of the tangent:
y’ = 2x - 1

2) Find x given that the gradient of the tangent is 3:
3 = 2x - 1
2x = 4
x = 2

3) Substitute x = 2 into the original equation:
y = x² - x + 1
   = 4 - 2 + 1
   = 3

Hope this helps

[sayma]

Hi can someone please help me with this question:
find the equation of the tangent to the curve y=1/3x at the point where x=1/6.
Thanks

[AngelWings]

find the equation of the tangent to the curve y=1/3x at the point where x=1/6.
Thanks

I believe you've missed a power here, because y = 1/3x is not exactly a curve, but a line. (Just letting you know. Try using the 'modify' button on your post with the mistake.)  
In order to solve it, it should be similar to the steps Jess1113 has stated previously, with the exception of finding y instead of x at Step 2 of her post.

[sayma]

Hey there, i double checked the question but there arent any powers anywhere. But do you think it will work if (1/3x) is differentiated using the  quotient rule?

[Shadowxo]

Hi can someone please help me with this question:
find the equation of the tangent to the curve y=1/3x at the point where x=1/6.
Thanks

It's a very similar process to Jess'
To find the equation of the tangent (which you know will be a line) you need to know the gradient and a point on the line. From there you can use y-y1 = m(x-x1)
To find the gradient, simply find the derivative and substitute in the x value (in this case, 1/6)
To find a point on the line, you know the tangent at x=1/6 touches the curve at x=1/6, so substitute this x value into the equation y=1/3x to find the y value where x=1/6. This will be a point on the line.

Hey there, i double checked the question but there arent any powers anywhere. But do you think it will work if (1/3x) is differentiated using the  quotient rule?

I think it was misinterpreted as (1/3)x which is a line, instead of 1/(3x) which is a curve.
You shouldn't need to use the quotient rule - use standard derivatives instead.
1/(3x) can be rewritten as
The quotient rule is best when there are two different expressions involving x on the top and bottom of a fraction, and product rule is for when two expressions involving x are multiplied together.

Note: the quotient and product rule will work even when it's not necessary to use them, it's just time consuming.

[AngelWings]

I think it was misinterpreted as (1/3)x which is a line, instead of 1/(3x) which is a curve.
You shouldn't need to use the quotient rule - use standard derivatives instead.
1/(3x) can be rewritten as

Whoops. Clearly been dealing with way too much Further Maths! My apologies.

[sayma]

Thanks for that Shadowxo, all g AngelWings