Find the derivative of f(x) = 12x^2 + 8x at x = 9.

224

Step-by-step explanation:

We will need the following rules for derivative:

Sum rule.

Constant multiple rule.

Power rule.

Slope of y=x is 1.

by sum rule.

by constant multiple rule.

by power rule.

Now we need to find the derivative function evaluated at x=9.

In case you wanted to use the formal definition of derivative:

Or the formal definition evaluated at x=a:

Let's use that a=9.

We need to find f(9+h) and f(9):

(used foil or the formula  (x+a)(x+a)=x^2+2ax+a^2)

Combine like terms:

Ok now back to our definition:

Simplify by doing 1044-1044:

Each term has a factor of h so divide top and bottom by h:

for future students the answer is b

hope i

-lavira: )