Question

Consider a function of the form f(x) = 7x^2 + ax, where a is a real number. What is the difference quotient of f(x) for all nonzero values of h?

A. 7h + a

B. 14x + 7h

C. 7x + 7h + a

D. 14x + 7h + a

Answer 1

Answer:

We select option D: 14 x + 7 h + a

Step-by-step explanation:

To find the difference quotient for h we do:

[f(x+h) - f(x) ] / h

that is:

[7 (x+h)^2 + a (x+h) - 7x^2 - a x] / h

[ 7 (x^2+ 2xh + h^2) - 7x^2 - a x] / h

[ 7 x^2 + 14 x h + 7 h^2 + ax + ah - 7 x^2 - a x] / h

cancel out terms:

[ 14 x h + 7 h^2 + ah] / h

14 x + 7 h + a