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Find 

f(a),  f(a + h), and the difference quotient f(a + h) − f(a)/h where h ≠ 0.

f(x) = 2x2 + 6

Guest Feb 7, 2018

Best Answer 

 #1
avatar+7089 
+3

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

 

\(\quad\,\frac{{\color{blue}f(a+h)}-{\color{purple}f(a)}}{h} \\~\\ =\,\frac{({\color{blue}2a^2+4ah+2h^2+6})-({\color{purple}2a^2+6})}{h} \\~\\ =\,\frac{2a^2+4ah+2h^2+6-2a^2-6}{h} \\~\\ =\,\frac{4ah+2h^2}{h} \\~\\ =\,\frac{h(4a+2h)}{h} \\~\\ =\,4a+2h\)

hectictar  Feb 8, 2018
 #1
avatar+7089 
+3
Best Answer

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

 

\(\quad\,\frac{{\color{blue}f(a+h)}-{\color{purple}f(a)}}{h} \\~\\ =\,\frac{({\color{blue}2a^2+4ah+2h^2+6})-({\color{purple}2a^2+6})}{h} \\~\\ =\,\frac{2a^2+4ah+2h^2+6-2a^2-6}{h} \\~\\ =\,\frac{4ah+2h^2}{h} \\~\\ =\,\frac{h(4a+2h)}{h} \\~\\ =\,4a+2h\)

hectictar  Feb 8, 2018

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