First slide

Tangents and normals

Question

$Which of the following points lies on the tangent to the curve x^{4} e^{y} + 2 \sqrt{y + 1} = 3 at the point$ $(1, 0) ?$

Easy

A

$(- 2, 6)$
B

$(- 2, 4)$
C

$(2, 2)$
D

$(2, 6)$

Solution

$x^{4} e^{y} + 2 \sqrt{y + 1} = 3$
Differentiating w.r.t ‘x’
$\begin{array}{l} x^{4} e^{y} y^{1} + 4 x^{3} e^{y} + \frac{1}{\sqrt{y + 1}} y^{1} = 0 \\ y^{1} + 4 + y^{1} = 0, a t (1, 0) ∣ \\ ∴ y^{1} = - 2 \end{array}$
Equation of tangent at (1,0) is
$\begin{array}{l} y = - 2 (x - 1) \\ 2 x + y = 2 \\ ∴ (- 2, 6) lies on this line \end{array}$

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