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Chapter 4: Problem 1

Find the slope of the tangent line to the exponential function at the point \((0,1) .\)

Short Answer

Expert verified
The slope of the tangent line to the function \( f(x) = e^x \) at the point (0,1) is 1.

Step by step solution

01

Write down the function and point

The function is \( f(x) = e^x \) and the point of interest is \( (0, 1) \). Note that the function \( f(x) = e^x \) passes through the point \( (0, 1) \).
02

Differentiate the function

The derivative of the function \( f(x) = e^x \) is also \( f'(x) = e^x \). The derivative provides the slope of the tangent line to the function at any given point.
03

Find the slope at the given point

Now that we have the derivative (which gives us the slope of the tangent at any point), we apply this to our point of interest: \( f'(0) = e^0 = 1 \).

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