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For the function f(x)=-9x-9, find the slope of the tangent line at x=-6. Answer:

For the function f(x)=−9x−9 f(x)=-9 x-9 , find the slope of the tangent line at x=−6 x=-6 .\newlineAnswer:

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Q. For the function f(x)=−9x−9 f(x)=-9 x-9 , find the slope of the tangent line at x=−6 x=-6 .\newlineAnswer:
  1. Identify Function Type: Identify the type of function and the method to find the slope of the tangent line.\newlineThe function f(x)=−9x−9f(x) = -9x - 9 is a linear function. The slope of the tangent line to a linear function is the same as the slope of the function itself.
  2. Determine Slope: Determine the slope of the function.\newlineFor a linear function in the form y=mx+by = mx + b, the slope is the coefficient of xx, which is mm. In this case, the slope of the function f(x)=−9x−9f(x) = -9x - 9 is −9-9.
  3. Calculate Tangent Line Slope: Since the slope of the function is constant, the slope of the tangent line at any point xx is the same as the slope of the function.\newlineTherefore, the slope of the tangent line at x=−6x = -6 is also −9-9.

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