Tangent Line Problem: Find Point P & Compute Slope m_L

[CrossFit415]

I'm on mobile so I can't use latex.

Let C: y=8x^5+5x+1 and suppose L is a line through the origin tangent to C at a point P=(a,f(a)) on C.

-Find the coordinates of P

-Compute the slope m sub L of L

Where should I begin? I'm guessing I would need the derivative of the equation f(x)? Then I would use the point slope form to figure out point P?

 

[Mark44]

I'm on mobile so I can't use latex.

Let C: y=8x^5+5x+1 and suppose L is a line through the origin tangent to C at a point P=(a,f(a)) on C.

-Find the coordinates of P

-Compute the slope m sub L of L

Where should I begin?

Maybe a sketch of the function?

I'm guessing I would need the derivative of the equation f(x)?

One would think that might somehow enter into things.

Then I would use the point slope form to figure out point P?

 

[CrossFit415]

After I sketch the eqiation what would I do after? So does that mean L is a secant line through the equation?

 

[Mark44]

L is a line that is tangent to the graph of the function. It's not a secant line (a line that hits a curve at two points).

BTW, "a secant line through the equation" doesn't make much sense, unless you actually draw a line through an equation, as opposed to drawing a line through the graph of an equation.

 

[CrossFit415]

L is a line that is tangent to the graph of the function. It's not a secant line (a line that hits a curve at two points).

BTW, "a secant line through the equation" doesn't make much sense, unless you actually draw a line through an equation, as opposed to drawing a line through the graph of an equation.

Haha I'll be more precise. I misread I thought it was going through the graph of the equation thinking its a secant line.

So I got the derivative which is f'(x) = (40x^4) + 5.

I wouldn't be able to apply the slope formula since I'm figuring out the coordinates of P. What methods are there?

 

[Mark44]

suppose L is a line through the origin tangent to C at a point P=(a,f(a)) on C.

So you have a line from (0, 0) to (a, f(a)) on the graph of your curve. Write an expression that represents the slope of the line.

Write another expression that represents the slope of the tangent at any point on your curve.

Equate the two expressions.