f'(x) is the derivative of the function, which is another function. Plugging in x1 gives the slope of the tangent line of the original function at x = x1
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Expression 6: "f" prime left parenthesis, "x" Subscript, 1 , Baseline , right parenthesisf′x1
equals=
67.567.5
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point slope form is used to write the tangent line. m= f'(x1), and (x,y) = (x1,f(x1))
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Expression 8: "y" minus "f" left parenthesis, "x" Subscript, 1 , Baseline , right parenthesis equals "f" prime left parenthesis, "x" Subscript, 1 , Baseline , right parenthesis left parenthesis, "x" minus "x" Subscript, 1 , Baseline , right parenthesisy−fx1=f′x1x−x1