find tangent line to curve and passing through point (1 Viewer)

[Symphonicity]

hi guys,

I thought I knew how to solve these sorts of problems but i keep getting the wrong answer. Please help me see where I'm going wrong.

So, the question asks me to find the equation of any tangent lines to the curve x^4-12x+50 that pass through the point (0,2). I start by finding the derivative which is 4x^3-12. This is the slope. Then I put the slope into the equation of a tangent formula

y-y1 = m (x-x1)

y-2 = 4x^3-12(x-0)

The problem arises because I end up with higher powers than just x^2 so I can't just factorise it and get two values for x.

Maybe these polynomials have to be approached differently. Any thoughts?

Thank you...

 

[bedpotato]

hi guys,

I thought I knew how to solve these sorts of problems but i keep getting the wrong answer. Please help me see where I'm going wrong.

So, the question asks me to find the equation of any tangent lines to the curve x^4-12x+50 that pass through the point (0,2). I start by finding the derivative which is 4x^3-12. This is the slope. Then I put the slope into the equation of a tangent formula
y-y1 = m (x-x1)

y-2 = 4x^3-12(x-0)

The problem arises because I end up with higher powers than just squares so maybe these polynomials have to be approached differently. Any thoughts?

Thank you...

This is where you started to go wrong. This not the slope, but the equation to find the slope at a specific point. So the question is asking for the equation of the tangent at (0,2). What is the gradient of the tangent at (0,2)? Sub 0 into the derivative, y = 4x^3 -12. You get -12.

Where m is, instead of 4x^3-12, sub in -12. Then it'll be a lot easier to find the equation!

 

[Symphonicity]

thanks for your response, but I'm still not getting the correct answer. The answers are y = 20x+2 and y = -44x + 2. The point (0,2), if I'm understanding the question correctly, is not on the curve. I assume at some point that I solve for x and get two values and end up with two answers, because the tangent lines fall on either side of the curve?

 

[bedpotato]

What exactly is the question asking?

Oh, okay I understand the question now. "Any tangent lines that pass through 0,2". I'll try it now.

 

[Symphonicity]

Sorry, I should have worded the question more clearly.

 

[Symphonicity]

Can I ask a supplementary question - what does this question mean? I'm having trouble understanding the problem.

"Find the point(s) on the graph of y=1/2x^2 at which the normal line passes through the point (4,1)"

I've found the slope (derivative) of the tangent to be x, so the slope of the normal I guess would be -x. I guess I then need to find the equation of the normal by substituting in m=-x and then finding points of intersection with the curve? is that right? The correct answer is (2,2) which suggests it only intersects once. I'm confused as on my drawing it looks like it should intersect twice.

Really appreciate your help.

 

[bedpotato]

Here you go. Hope you understand what I did.


The picture is cutting off from the bottom. But what you do is sub m (20 and -44) into the equation, y = mx + 2 and you will get the anwer. y = 20x + 2 and y = -44x + 2.

 

[cookiez69]

Can I ask a supplementary question - what does this question mean? I'm having trouble understanding the problem.

"Find the point(s) on the graph of y=1/2x^2 at which the normal line passes through the point (4,1)"

I've found the slope (derivative) of the tangent to be x, so the slope of the normal I guess would be -x. I guess I then need to find the equation of the normal by substituting in m=-x and then finding points of intersection with the curve? is that right? The correct answer is (2,2) which suggests it only intersects once. I'm confused as on my drawing it looks like it should intersect twice.

Really appreciate your help.

The gradient of the normal is -1/x not -x.

 

[Symphonicity]

Just been looking at your result. Thanks very much, I think I was halfway there but just not knowing how to do that last bit. I really appreciate that!!

 

[Symphonicity]

The gradient of the normal is -1/x not -x.

AH! got it. My method was correct but one little slip sent me astray. Now I get x=2 and y=2. YAY.