Math 172 , College Algebra

Question

For the function , evaluate and fully simplify each of the following. =     =  

Answer 1

The difference quotient:[ f(x+h) - f(x)] / h

f(x+h) = 5(x+h)^2 - 3(x+h) + 3

= (x+h) {5(x+h)-3} + 3

= (x+h) {5x+5h - 3}+ 3

= 5x^2 + 5xh - 3x + 5xh + 5h^2 - 3h + 3

= 5x^2 + 10xh - 3x + 5h^2 - 3h + 3

f(x+h) - f(x) = 10xh + 5h^2 - 3h

dividing by h

10x + 5h - 3