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Problem 10

# Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. $$f(x)=-6$$

Expert verified
The slope of the tangent line to the graph of the given function $$f(x) = -6$$ at any point is 0, as the function is a constant and its derivative $$f'(x)$$ is 0.
See the step by step solution

## Step 1: Write the function

We have the function $$f(x) = -6$$.

## Step 2: Find the derivative

To find the slope of the tangent line, we need to find the derivative of the function. Since the function is constant, the derivative is: $f'(x) = 0$

## Step 3: Plug in the point

Because the function is a constant, the slope of the tangent line will be the same at every point. Therefore, it doesn't matter which specific point we plug into the derivative to find the slope.

## Step 4: Find the slope

We have the derivative $$f'(x) = 0$$. So the slope of the tangent line to the graph of the function at any point is: $m = 0$ So, the slope of the tangent line to the graph of the function $$f(x) = -6$$ at any point is 0.

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