given g(x), find??

Question

Given g(x) = 3x2 - 3x + 11, find [g(a + h) - g(a)]/h.

How do I start? I'm soo confused, please help me!!

Answer 1

first, (x) is a or h or whatever you want it to be. g(x) is the function of x. so, that means, that for the 1st term in your problem, this is what you do:
g(a+h)= 3(a+h)^2 -3(a+h) +11
g(a+h)= 9a+9h-3a-3h+11

g(a+h)= 6a+6h+11

g(a)= 6a+11

then you subtract, so what's left is 6h
divide 6h by h, and you get...
6

there you go, hope I helped!

Answer 2

Think about this: If g(x)=3x^2 -3x+11, then g(a+h)=3(a+h)^2 -3(a+h)+11. The same applies for g(a). Just substitute the value in the parentheses for x and solve for g(a+h) and g(a).

Once you find those, you can solve for [g(a+h)-g(a)]/h

Answer 3

Do it exactly as the formula says:

( (3(a+h)^2+3(a+h)+11) - (3(a)^2+3(a)+11) ) / h

You'll get the result:

6a - 3 + 3h