Find the difference quotient g(x) =5x^2+9x-5
The difference quotient for the function g(x) = 5x^2 + 9x - 5 is given by:
[g(x + h) - g(x)] / h
Substituting the function into the difference quotient formula, we get:
[(5(x + h)^2 + 9(x + h) - 5) - (5x^2 + 9x - 5)] / h
Expanding the terms and simplifying, we get:
[5(x^2 + 2xh + h^2) + 9x + 9h - 5 - 5x^2 - 9x + 5] / h
Simplifying further, we get:
[5x^2 + 10xh + 5h^2 + 9x + 9h - 5 - 5x^2 - 9x + 5] / h
The x^2 terms cancel out:
[10xh + 5h^2 + 9h] / h
Further simplifying, we get:
(10xh + 5h^2 + 9h) / h
Factoring out an h, we get:
h(10x + 5h + 9) / h
The h terms cancel out:
10x + 5h + 9
So, the difference quotient for g(x) = 5x^2 + 9x - 5 is 10x + 5h + 9.