Evaluate the difference quotient for the given function. Simplify your answer. f(x) = 4 + 3x - x^2, (f(3+h) - f(3))/h
1 Answer
justaguide | College Teacher | (Level 2) Distinguished Educator
The function f(x), is defined as f(x) = 4 + 3x - x^2.
To determine the difference quotient `(f(3+h) - f(3))/h` , determine the expression for f(3 + h), f(3), subtract the latter from the former and divide the final result by h.
`(f(3+h) - f(3))/h`
= `(4 + 3*(3+h) - (3+h)^2 - (4 + 3*3 - 3^2))/h`
= `(4 + 9 + 3h - 9 - h^2 - 6h - 4 - 9 + 9)/h`
= `(3h - 9 - h^2 - 6h + 9)/h`
= `(-h^2 - 3h)/h`
= -h - 3
= -3