Question

Find the slope of the tangent line to the curve f(x)=e^(x) at (0.4,1.49)

Answer 1

1.49

Explanation:

In order to find the slope of the tangent line to a given equation, and in a given point, we need to:

1. Find the first derivative of the given function.

2. Evaluate the first derivative function in the given point.

1. Let's find the first derivative of the given function:

The original function is
`f(x)=e^(x)`

But remeber that the derivative of
`e^(x)` is
`e^(x)`

so,
`f'(x)=e^(x)`

2. Let's evaluate the first derivative function in the given point

The given point is (0.4,1.49) so:

`f'(x)=e^(x)`

`f'(0.4)=e^(0.4)`

`f'(x)=1.49`

Notice that the calculated slope of the tangent line is equal to the y-coordinate of the given point because f'(x)=f(x). In conclusion, the slope of the tangent line is equal to 1.49.