# Tangent line

Dustinsfl
For what value of b is the line y = 10x tangent to the curve y = e$$^{bx}$$ at some point in the xy-plane?

y' = b*e$$^{bx}$$ = 10x

How can I solve for b here?

## Answers and Replies

Homework Helper
Gold Member
For what value of b is the line y = 10x tangent to the curve y = e$$^{bx}$$ at some point in the xy-plane?

y' = b*e$$^{bx}$$ = 10x

How can I solve for b here?

Your equation isn't right.

What condition(s) must be satisfied if $y = 10x$ is tangent to $y = e^{bx}$ at some point?

Dustinsfl
It has to be the derivative.

Homework Helper
Gold Member
It has to be the derivative.

What has to be what derivative? Try to be precise when you are expressing ideas in mathematics.

Say I have two differentiable functions, $f(x)$ and $g(x)$. What must be true if $g$ is tangent to $f$ at some point $x_0$?

Dustinsfl
I already solved for the derivative in my 1st post and set it equal to the tangent equation since the derivative needs to equal that to satisfy the problem. The problem was that I have b times e to the b where I need to solve for b.

Homework Helper
Gold Member
I already solved for the derivative in my 1st post and set it equal to the tangent equation since the derivative needs to equal that to satisfy the problem. The problem was that I have b times e to the b where I need to solve for b.

As I already said, your equation is wrong, so there is no point trying to solve it for b.

Can you explain why you set the derivative of the exponential equal to 10x?

Dustinsfl
That is what I need the derivative to be equal.

Homework Helper
Gold Member
That is what I need the derivative to be equal.

No it's not.

What properties of a curve and a line must be equal if the line is to be tangent to the curve at a point?

Dustinsfl
We can keep going around and circles all day but it isn't going to get anywhere.

Homework Helper
Gold Member
We can keep going around and circles all day but it isn't going to get anywhere.

OK, good luck.

justsof
We can keep going around and circles all day but it isn't going to get anywhere.

"We" ? You are the one thinking in circles, jbunniii is actually trying to point you the way out of your circles, but it seems you just don't want to listen...