Question

Find f(a), f(a+h), and the difference quotient f(a+h)-f(a), where h +0.
h
f(x) = 5x² + 2
f(a) =
f(a+h) =
f(a+h)-f(a) =
h

Answer 1

$f(a)=\boxed{5a^{2}+2}\\\\f(a+h)=5(a+h)^{2}+2=5(a^{2}+2ah+h^{2})+2=\boxed{5a^2 + 10ah+5h^2 +2}\\\\f(a+h)-f(a)=(5a^2 + 10ah+5h^2 +2)-(5a^2 +2)=\boxed{10ah+5h^2}$