Answer :
Final answer:
The correct derivative of the function f(x) = x³ - 27x + 9 is 3x² - 27.
Explanation:
In mathematics, the derivative of a function measures how that function changes as the variables change. Given the function f(x)=x³−27x+9, to find the derivative, apply the power rule, which states that the derivative of xⁿ is n×xⁿ⁻¹. Also, the derivative of a constant times x is the constant. Therefore, the derivative of x³ is 3x² the derivative of -27x is -27, and the derivative of the constant 9 is 0 since constants don't affect rates of change. So, the derivative of f(x) is 3x²−27. Thus, among options you've listed, Option 1: 3x²−27 is correct. The other options are incorrect because they do not match the calculated derivative.
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