Find an equation for the tangent line of y = e 2 x that is parallel to the linear equation y = 7 x + 13 . Provide your answer in slope–intercept form of a linear equation, y = m x + b , where m is the slope and b is the y - intercept. Express m and b as exact numbers.

Step-by-step explanation:

We are asked to find equation of tangent line of function that is parallel to the linear equation .

First of all, we will find the derivative of given function applying chain rule as:

Since derivative represents slope or rate of change, so we will equate derivative to slope of line   and solve for x as:

Now, we will substitute in equation to find value of y as:

Applying log property , we will get:

Now, we will substitute , and in point slope form as:

Therefore, the equation of the tangent line would be .

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step-by-step explanation:

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the correct answer is the second option