91Ó°ÊÓ

In this test: Unless otherwise specified, the domain of a function \(f\) is assumed to be the set of all real numbers \(x\) for which \(f(x)\) is a real number. If \(3 x^{2}-2 x y+3 y=1,\) then when \(x=2, \frac{d y}{d x}=\) (A) \(-12\) (B) \(-10\) (C) \(-\frac{10}{7}\) (D) \(12\)

In this test: Unless otherwise specified, the domain of a function \(f\) is assumed to be the set of all real numbers \(x\) for which \(f(x)\) is a real number. \(\int_{1}^{3} \frac{8}{x^{3}} d x=\) (A) \(\frac{32}{9}\) (B) \(\frac{40}{9}\) (C) 0 (D) \(-\frac{32}{9}\)

In this test: Unless otherwise specified, the domain of a function \(f\) is assumed to be the set of all real numbers \(x\) for which \(f(x)\) is a real number. If \(f(x)=\int_{0}^{x+1} \sqrt[3]{t^{2}-1},\) then \(f^{\prime}(-4)=\) (A) \(-2\) (B) 2 (C) \(\sqrt[3]{15}\) (D) 0

In this test: Unless otherwise specified, the domain of a function \(f\) is assumed to be the set of all real numbers \(x\) for which \(f(x)\) is a real number. The value of \(c\) that satisfies the Mean Value Theorem for derivatives on the interval \([0,5]\) for the function \(f(x)=x^{3}-6 x\) is (A) 0 (B) 1 (C) \(\frac{5}{3}\) (D) \(\frac{5}{\sqrt{3}}\)