Simplify (f(a+h)-fa)/h

Problem

(ƒ*(a+h)−ƒ(a))/h

Solution

1. Identify the expression as the difference quotient, which represents the average rate of change of a function ƒ over the interval [a,a+h]

2. Evaluate the function ƒ at the inputs a+h and a to find the change in the output values.

3. Subtract the value ƒ(a) from ƒ*(a+h) to determine the numerator, which represents the total change in the function.

4. Divide the result by h which represents the change in the input values.

5. Simplify the resulting fraction by canceling any common factors of h if the specific form of ƒ(x) is provided.

Final Answer

(ƒ*(a+h)−ƒ(a))/h=(ƒ*(a+h)−ƒ(a))/h

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