For the function f(x)=x249f(x)=x2-49, evaluate f(x+h)f(x+h)

 

 

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f(x+h)=(x+h)²-49=x²+2xh+h²-49.

Note that f(x+h)—f(x)=2xh+h² and f(x+h)/h=2x+h which becomes 2x as h→0. 2x is the derivative of f(x)=x²-49.

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