# Tangent line

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?

jbunniii
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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?

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

It has to be the derivative.

jbunniii
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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 $x_0$?

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.

jbunniii
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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?

That is what I need the derivative to be equal.

jbunniii
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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?

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

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

OK, good luck.

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...