Given the quadratic function f(x)=6x^2+5x

Question

Given the quadratic function f(x)=6x^2+5x

Compute f(a+h) − f(a)=______

Assuming h≠0, compute f(a+h) − f(a)/h = ____

Answer 1

f(a+h) = 6(a+h)^2 + 5(a+h) = 6( a^2 +2ah +h^2) + 5a+5h = 6a^2 + 12ah + 6h^2 +5a+5h

f(a) = 6a^2+5a

Therefore,

f(a+h)-f(a) = ( 6a^2 + 12ah + 6h^2 +5a+5h ) - ( 6a^2+5a ) = 12ah +6h^2+5h

Provided that h is not zero,

( f(a+h)-f(a) ) / h = (12ah +6h^2+5h)/h = 12a +5+6h