Find the Difference Quotient f(x)=-3x+1

Problem

ƒ(x)=−3*x+1

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 expression ƒ*(x+h) by substituting x+h into the original function for every instance of x

ƒ*(x+h)=−3*(x+h)+1

3. Distribute the constant −3 into the parentheses.

ƒ*(x+h)=−3*x−3*h+1

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

((−3*x−3*h+1)−(−3*x+1))/h

5. Simplify the numerator by distributing the negative sign and combining like terms.

(−3*x−3*h+1+3*x−1)/h

(−3*h)/h

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

−3

Final Answer

(ƒ*(x+h)−ƒ(x))/h=−3

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