2 Answers

WalterM · Answer 1 · 2021-07-09T05:13:25+0000

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

$\lim_(h\to 0) (f(x+h)-f(x))/h =4\cdot 9^3 = 2916$

Answer: Choice C, 2916

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