Find
f(a), f(a + h), and the difference quotient f(a + h) − f(a)/h where h ≠ 0.
f(x) = 2x2 + 6
+9466 f(x) = 2x2 + 6
f(a) = 2a2 + 6
f(a + h) = 2(a + h)2 + 6
f(a + h) = 2(a + h)(a + h) + 6
f(a + h) = 2(a2 + 2ah + h2) + 6
f(a + h) = 2a2 + 4ah + 2h2 + 6
\(\quad\,\frac{{\color{blue}f(a+h)}-{\color{purple}f(a)}}{h} \\~\\ =\,\frac{({\color{blue}2a^2+4ah+2h^2+6})-({\color{purple}2a^2+6})}{h} \\~\\ =\,\frac{2a^2+4ah+2h^2+6-2a^2-6}{h} \\~\\ =\,\frac{4ah+2h^2}{h} \\~\\ =\,\frac{h(4a+2h)}{h} \\~\\ =\,4a+2h\)
+9466 f(x) = 2x2 + 6
f(a) = 2a2 + 6
f(a + h) = 2(a + h)2 + 6
f(a + h) = 2(a + h)(a + h) + 6
f(a + h) = 2(a2 + 2ah + h2) + 6
f(a + h) = 2a2 + 4ah + 2h2 + 6
\(\quad\,\frac{{\color{blue}f(a+h)}-{\color{purple}f(a)}}{h} \\~\\ =\,\frac{({\color{blue}2a^2+4ah+2h^2+6})-({\color{purple}2a^2+6})}{h} \\~\\ =\,\frac{2a^2+4ah+2h^2+6-2a^2-6}{h} \\~\\ =\,\frac{4ah+2h^2}{h} \\~\\ =\,\frac{h(4a+2h)}{h} \\~\\ =\,4a+2h\)
