Find the Slope x=-4

Problem

y=1/x

Solution

1. Identify the function to be differentiated. The task asks for the slope of the function y=1/x at the point where x=−4

2. Find the derivative of the function with respect to x to determine the general formula for the slope. Using the power rule where 1/x=x(−1)

d(y)/d(x)=d()/d(x)*x(−1)

d(y)/d(x)=−1*x(−2)

d(y)/d(x)=−1/(x2)

3. Substitute the given value x=−4 into the derivative to find the specific slope at that point:

m=−1/((−4)2)

4. Simplify the resulting value:

m=−1/16

Final Answer

d(y)/d(x)|=−1/16

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