Simplify Quotient of f(x) and Find Values of a and b | Derivative Question

[TrueStar]

Homework Statement

Let f(x) be the function 6x²-3x+11 . Then the quotient f(6+h)-f(6) / h can be simplified to ah+b for what value of a and what value of b?

Homework Equations

I think I need to simplify the quotient above.

The Attempt at a Solution

I know that a=6. I'm not sure what b is supposed to be, nor am I sure what the question is asking me exactly. Perhaps if someone could clarify what I'm supposed to be looking for, it'd give me a push in the right direction.

Thanks!

 

[Office_Shredder]

Have you tried evaluating f(6+h)-f(6) / h and seeing what you get?

 

[TrueStar]

I would get 1 (one), correct?

 

[Mark44]

I would get 1 (one), correct?

No, you're way off. You have the formula for the function, so evaluate [f(6 + h) - f(6)]/h.

 

[TrueStar]

OK, I set up the expression as (6+h)^2-3(6+h)+11-6 / h

From this, I got 6h+272

Is this the correct method?

 

[Dick]

OK, I set up the expression as (6+h)^2-3(6+h)+11-6 / h

From this, I got 6h+272

Is this the correct method?

Sort of, except you are making a lot of mistakes. It's 6*(6+h)^2-3*(6+h)+11-f(6) in the numerator. And f(6) isn't 6.

 

[TrueStar]

I was working at this problem over dinner with friends and one of my friend's girlfriend happened to see me. She's a math tutor and she showed me the mistakes I was making. I know now that it works out to 6h+69. Thank you all for the added help; I am sorry for being frustrating with my obvious mistakes. :/