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Chapter 4: Problem 2

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 exponential function at the point (0,1) is 1.

Step by step solution

01

Identify the function

Given that the value of the function at x=0 is 1, we can assume that the function is \( y = e^x \). The reason is \( e^0 = 1 \)
02

Differentiate the function

The derivative of the function \( y = e^x \) is also \( y' = e^x \). This is due to the unique property of the exponential function where it is equal to its own derivative.
03

Calculate the slope of the tangent line

The slope of the tangent is given by the derivative at that point. Substituting x=0 in the derivative, we get \( y' = e^0 \), which simplifies to \( y' = 1 \)

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