SOLUTION: For the function f(x)= -3x^2 + x- 11, determine the difference quotient f(a+h) - f(a)/h where h is not equal to 0. Simplify your result as much as possible.

Question 87218: For the function f(x)= -3x^2 + x- 11, determine the difference quotient
f(a+h) - f(a)/h where h is not equal to 0. Simplify your result as much as possible.
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
lim( h -> 0 ) ( f(a + h) - f(a) ) / h
lim( h -> 0 ) ( -3(a + h)^2 + (a + h) - 11 + 3a^2 - a + 11 ) / h
lim( h -> 0 ) ( -3(a^2 + 2ah + h^2) + a + h - 11 + 3a^2 - a + 11 ) / h
lim( h -> 0 ) ( -3a^2 - 6ah - 3h^2 + h + 3a^2 ) / h
lim( h -> 0 ) ( -6ah - 3h^2 + h ) / h
lim( h -> 0 ) -6a - 3h + 1
~Derive~
lim( h -> 0 ) -6a - 3(0) + 1 = -6a + 1
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