Final answer:
To compute the given expression, substitute the given function and simplify the expression by canceling out common factors.
Step-by-step explanation:
To compute the expression (f(x+h)-f(x))/(h)(h)! for the given function f(x)=7x^2+6x, we need to substitute the function into the expression and simplify.
First, let's substitute the given function into the expression:
(f(x+h)-f(x))/(h)(h)! = (7(x+h)^2+6(x+h) - (7x^2+6x))/(h)(h)!
Expanding and simplifying the expression further, we get:
(7x^2+14hx+7h^2+6x+6h-7x^2-6x)/(h)(h)! = (14hx+7h^2+6h)/(h)(h)!
Simplifying the expression by canceling out common factors, we have:
(14x+7h+6)/(h)!
Therefore, the expression is equal to (14x+7h+6)/(h)!.