iran-konkur 2018 Q119

iran-konkur · Other · konkur-riazi_1397_specialized Implicit equations and differentiation Second derivative via implicit differentiation
119- From the relation $y^2 + xy^2 + x = 7$, the value of $\dfrac{d^2y}{dx^2}$ at the point $(1,2)$ is which of the following?
(1) $\dfrac{3}{4}$ (2) $\dfrac{4}{5}$ (3) $\dfrac{6}{5}$ (4) $\dfrac{3}{2}$

120- The function $f : \mathbb{R} \to \mathbb{R}$ is twice differentiable. For every real number $x$, the function $g(x) = f(4 - x^2)$ is defined. If $f^{-1}(1) = -5$ and $f^{-1}(1) = -1$, and $f''(1) = -1$, what is the value of $g''(\sqrt{3})$?
(1) $-3$ (2) $-2$ (3) $2$ (4) $3$
\textbf{119-} From the relation $y^2 + xy^2 + x = 7$, the value of $\dfrac{d^2y}{dx^2}$ at the point $(1,2)$ is which of the following?

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\hspace{1cm} (1) $\dfrac{3}{4}$ \hspace{2.5cm} (2) $\dfrac{4}{5}$ \hspace{2.5cm} (3) $\dfrac{6}{5}$ \hspace{2.5cm} (4) $\dfrac{3}{2}$

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\textbf{120-} The function $f : \mathbb{R} \to \mathbb{R}$ is twice differentiable. For every real number $x$, the function $g(x) = f(4 - x^2)$ is defined. If $f^{-1}(1) = -5$ and $f^{-1}(1) = -1$, and $f''(1) = -1$, what is the value of $g''(\sqrt{3})$?

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\hspace{2cm} (1) $-3$ \hspace{2cm} (2) $-2$ \hspace{2cm} (3) $2$ \hspace{2cm} (4) $3$

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