Question

For the function f(x)=3x²−3x, evaluate and simplify the expression f(x+h)−f(x)-f(x)/(h) = 6hx+3h²−3h. What is the correct simplified result?

Answer 1

The simplification of the expression f(x+h)−f(x) for the function f(x)=3x²−3x is correctly simplified to 6hx+3h²−3h when expanded and like terms are cancelled out.

Step-by-step explanation:

The student has asked to evaluate and simplify the expression f(x+h)−f(x) for the function f(x)=3x²−3x, and to verify if the given simplification 6hx+3h²−3h is correct.

Let's simplify f(x+h)−f(x) step by step:

1. Firstly, calculate f(x+h), which would be f(x+h) = 3(x+h)² − 3(x+h).
2. Expand the squared term and distribute the 3, resulting in 3x²+6hx+3h² − 3x − 3h.
3. Now, find f(x), which is 3x² − 3x.
4. Subtract f(x) from the expanded f(x+h), yielding (3x²+6hx+3h² − 3x − 3h) - (3x² − 3x).
5. Cancel out the like terms to get the simplified result: 6hx+3h² − 3h.

Hence, the simplification provided in the question, 6hx+3h²−3h, is indeed correct.