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enyata [817]
3 years ago
5

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

Mathematics
1 answer:
almond37 [142]3 years ago
8 0

Answer:

1.49

Step-by-step 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.

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