Find the Difference Quotient f(x)=2x^2-x+3

Problem

ƒ(x)=2*x2−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 ƒ*(x+h) by substituting x+h into the original function for every instance of x

ƒ*(x+h)=2*(x+h)2−(x+h)+3

3. Expand the squared binomial and distribute the constants and signs.

ƒ*(x+h)=2*(x2+2*x*h+h2)−x−h+3

ƒ*(x+h)=2*x2+4*x*h+2*h2−x−h+3

4. Subtract ƒ(x) from ƒ*(x+h) to find the numerator of the difference quotient.

ƒ*(x+h)−ƒ(x)=(2*x2+4*x*h+2*h2−x−h+3)−(2*x2−x+3)

5. Simplify the numerator by canceling out the terms 2*x2 −x and 3

ƒ*(x+h)−ƒ(x)=4*x*h+2*h2−h

6. Divide the simplified numerator by h

(4*x*h+2*h2−h)/h

7. Factor out h from the numerator and cancel it with the h in the denominator.

(h*(4*x+2*h−1))/h=4*x+2*h−1

Final Answer

(ƒ*(x+h)−ƒ(x))/h=4*x+2*h−1

Want more problems? Check here!