That's the derivative at x=9 so will be 4(9³)=2916. Let's do it the hard way.
f(x) = x⁴
f(9)=9⁴
f(9+h)=(9+h)⁴ = 9⁴ +4·9³ h + 6·9²h² + 36h³ + h⁴
(f(9+h)-f(9))/h = 4·9³ + 6·9²h + 4·9h² + h³
[tex]\lim_{h\to 0} (f(x+h)-f(x))/h =4\cdot 9^3 = 2916[/tex]
Answer: Choice C, 2916
