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Determine the equation of the tangent line at the given $x$ -coordinate.$$f(x)=e^{x}, x=0$$

$y=x+1$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 4

The Derivative of the Exponential Function

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anytime were asked to find a tangent line. Basically, what we're saying is we need a point and a slope. Well, the nice thing about this problem is they give you the the X coordinate of the 0.0, Eh? So what, you have to figure out the y coordinate. Well, that's not too bad, because the equation is e to the X power. Uh, so if you plug zero in for X, Okay, so, uh, under this in red E to the zero power they expect you didn't know is one. Uh, the other reason why that's kind of nice is because this is basically your why intercept. So when you get to point slope form, it's really easy to come up with. So then the slope, that's the derivative when x zero. Well, we can figure that out because the derivative of this function is e to the x power and, uh, way just did the work. Either the zero power equals one. So what that means is, when you write the equation, y equals MX plus B. We just figured out the slope is one. And then the y intercept the B value is one. So that's your answer.

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