- #1

rakalakalili

- 14

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## Homework Statement

Hello, this is a problem from the practice test for the GRE subject test.

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

A) [tex]\frac{10}{e}[/tex]

B)10

C)10e

D)[tex]e^{10}[/tex]

E)e

## Homework Equations

## The Attempt at a Solution

For the line to be tangent to the curve, they must intersect at a point and their derivatives must be equal. So we get a system of equations:

[tex]10x=e^{bx}[/tex]

[tex]10=be^{bx}[/tex]

But I cannot think of a way to solve this system easily. Would the best method be to simply plug in the possible answers and check? This seems time consuming, and since this is a practice GRE question I am interested in the simplest way of solving it. Please let me know if I am over looking something, thank you!