1. Tangent line problem

The two tangents that can be drawn from the point (3,5) to the parabola y=x^2 have slopes?

-my steps
y'=2x
I know this is sad. But i just don't know what the question is asking i usually have all the tangent line questions down but this one is stumping me.

The line y=3x+k is tangent to the curve y=x^3 when k is equal to?
-my steps
y'=2x
2x=3x+k
this doesn't make any sense and i think i am doing it wrong.

All help is appreciated. Thanks

2. Originally Posted by dandaman
The two tangents that can be drawn from the point (3,5) to the parabola y=x^2 have slopes?

-my steps
y'=2x
I know this is sad. But i just don't know what the question is asking i usually have all the tangent line questions down but this one is stumping me.

The line y=3x+k is tangent to the curve y=x^3 when k is equal to?
-my steps
y'=2x
2x=3x+k
this doesn't make any sense and i think i am doing it wrong.

All help is appreciated. Thanks
You were right by taking the derivative. The equation you got was:

$m = y' = 2x$

So for the point (3,5) you can use the equation we found from the derivative to calculate the slope at that point.

$(y-5) = m(x-3)$ *substitute your slope from the derivative in for m

$(y-5)= (2x)(x - 3)$

$y = 2x^2-6x+5$

Then substitute this equation back into your original equation for y.

$2x^2 - 6x + 5 = x^2$

Get everything on one side and then find your x values either by factoring or quadratic formula.

This will give you two x values on the two tangent lines. You can simply plug each of these into your slope equation m = 2x and that will give your their slopes.

Using this info, see if you can work out the second one. Hope that helps!

3. for the first one i got 1 and 5. Is this right?

As for the second one,

m=y'=3x^2
so x must be at 1 since 3x^2=3x at x=1
then k=0
Is this right?

4. Originally Posted by dandaman
for the first one i got 1 and 5. Is this right?

As for the second one,

m=y'=3x^2
so x must be at 1 since 3x^2=3x at x=1
then k=0
Is this right?