iran-konkur 2020 Q121

iran-konkur · Other · konkur-riazi_1399_specialized_old-curriculum Tangents, normals and gradients Geometric properties of tangent lines (intersections, lengths, areas)
121. The tangent line to the curve $f(x) = \dfrac{5x - 4}{\sqrt{x}}$ at the point $x = 4$. At which values does it intersect the $y$-axis?
(1) $-4$ (2) $-1$ (3) $2$ (4) $3$

122. If $\tan\alpha$ and $\tan\beta$ are the roots of the equation $2x^2 + 3x - 1 = 0$, what is $\tan(\alpha + \beta)$?
(1) $1$ (2) $\dfrac{3}{2}$ (3) $-3$ (4) $-1$
\textbf{121.} The tangent line to the curve $f(x) = \dfrac{5x - 4}{\sqrt{x}}$ at the point $x = 4$. At which values does it intersect the $y$-axis?

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(1) $-4$ \hfill (2) $-1$ \hfill (3) $2$ \hfill (4) $3$

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\textbf{122.} If $\tan\alpha$ and $\tan\beta$ are the roots of the equation $2x^2 + 3x - 1 = 0$, what is $\tan(\alpha + \beta)$?

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(1) $1$ \hfill (2) $\dfrac{3}{2}$ \hfill (3) $-3$ \hfill (4) $-1$

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