Find the Difference Quotient f(x)=4x+3

Problem

ƒ(x)=4*x+3

Solution

1. Identify the formula for the difference quotient, which is defined as (ƒ*(x+h)−ƒ(x))/h for h≠0

2. Evaluate the function at x+h by substituting x+h into the original expression for every x

ƒ*(x+h)=4*(x+h)+3

3. Distribute the constant 4 into the parentheses.

ƒ*(x+h)=4*x+4*h+3

4. Substitute the expressions for ƒ*(x+h) and ƒ(x) into the difference quotient formula.

((4*x+4*h+3)−(4*x+3))/h

5. Simplify the numerator by removing parentheses and combining like terms.

(4*x+4*h+3−4*x−3)/h

(4*h)/h

6. Divide the numerator by h to find the final result.

4

Final Answer

(ƒ*(x+h)−ƒ(x))/h=4

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