# How do you find the slope of a tangent line to the graph of the function # f(x) = 2e^(-3x)# at (0, 2)?

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To find the slope of a tangent line to the graph of a function at a specific point, you can use the derivative of the function. In this case, the function is f(x) = 2e^(-3x). To find the slope of the tangent line at the point (0, 2), you need to find the derivative of f(x) and evaluate it at x = 0.

The derivative of f(x) = 2e^(-3x) can be found using the chain rule. The derivative is given by f'(x) = -6e^(-3x).

To find the slope of the tangent line at x = 0, substitute x = 0 into the derivative: f'(0) = -6e^(-3(0)) = -6e^0 = -6.

Therefore, the slope of the tangent line to the graph of f(x) = 2e^(-3x) at the point (0, 2) is -6.

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