Answer:
Step-by-step explanation:
f(x) = (2x^2 + 1)
( f(3 + h) - f(3) ) / h
f(3 + h) = 2(3 + h)^2 + 1)
f(3 + h) = 2(9 + 6h + h^2) + 1
f(3 + h) = 18 + 12h + 2h^2 + 1
f(3 + h) = 19 + 12h +2h^2
f(3) = 2*(3^2) + 1
f(3) = 2(9) + 1
f(3) = 19
f(3 + h) - f(3) = 2h + 2h^2 The 19s cancel out
f(3 + h) - f(3) = 2h(1 + h^2)
( f(3 + h) + f(3) ) / h = 2h ( 1 + h^2) / h = 2 ( 1 + h^2)
