How to find the difference quotient

Question

Hi, how do you solve this?

Find the difference quotient of 𝑓(𝑥) for the following function. Be sure to simplify.

𝑓(𝑥)= −3𝑥2 −6𝑥+1

Answer 1

The difference quotient is (1/h)[f(x+h)-f(x)].

Put x+h and x into the function, subtract the two expressions and divide by h.

Be careful with your algebra!

When you get the result you should see that the limit of the difference quotient is -6x-6!