SOLUTION: Given f(x) = 2x² + 3x - 1 Find and simplify: {{{(f(a+h) - f(a))/h}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Given f(x) = 2x² + 3x - 1 Find and simplify: {{{(f(a+h) - f(a))/h}}}       Log On


   

Question 887179: Given f(x) = 2x² + 3x - 1
Find and simplify: %28f%28a%2Bh%29+-+f%28a%29%29%2Fh
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Parentheses Added for the Numerator.

Just form the expression and simplify!

%282%28a%2Bh%29%5E2%2B3%28a%2Bh%29-1-%282a%5E2%2B3a-1%29%29%2Fh, which is only simple substituting. Working into that,
%282%28a%5E2%2B2ah%2Bh%5E2%29%2B3a%2B3h-1-2a%5E2-3a%2B1%29%2Fh
%282a%5E2%2B4ah%2B2h%5E2%2B3a%2B3h-2a%5E2-3a%29%2Fh
%284ah%2B2h%5E2%2B3a%2B3h-3a%29%2Fh
%284ah%2B2h%5E2%2B3h%29%2Fh
highlight%284a%2B2h%2B3%29




---
Much later, you will be interested in what happens to the final expression as h approaches 0. The result would be that the difference quotient approaches 4a%2B3.