Question

Find f(a+h)-f(a) for the function. Simplify your answer. f(x)=6+x^(2)

Answer 1

Explanation:

We can use the difference quotient rule to find the difference between the values of f(a+h) and f(a):

f(a+h)-f(a) = f'(a)h

Where h is the change in x.

For f(x)= 6 + x^2:

f'(x) = 2x

Substituting for a = 2:

f(2+h)-f(2) = 2(2+h)

Simplifying, we have:

f(2+h)-f(2) = 4 + 2h

Therefore, the difference between f(a+h) and f(a) for f(x) = 6 + x^2 is 4 + 2h.