Consider the function f(x) = x-4x+1. a) Simplify the expression f(x+h)-f(x) h for the given function....

 

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Consider the function f(x) = x-4x+1. a) Simplify the expression f(x+h)-f(x) h for the given function. b) What will happen to the expression in part a) when h becomes very close to zero? c) Use the simplified expression from part a) to estimate the instantaneous rate of change at x=1, x=2, and x=3. Explain what these results tell you about the function. Consider the function f(x) = x-4x+1. a) Simplify the expression f(x+h)-f(x) h for the given function. b) What will happen to the expression in part a) when h becomes very close to zero? c) Use the simplified expression from part a) to estimate the instantaneous rate of change at x=1, x=2, and x=3. Explain what these results tell you about the function.