First slide

Tangents and normals

Question

$The point on the graph of the curve y = (x - 3)^{2}, where the tangent is parallel to the line$ $joining of (3,0), (4, 1) is$

Moderate

A

$(\frac{7}{2}, \frac{1}{4})$
B

$(1, 4)$
C

$(2, 1)$
D

$(\frac{1}{2}, \frac{25}{4})$

Solution

$\begin{array}{l} \frac{d y}{d x} = \frac{1 - 0}{4 - 3} \\ \Rightarrow 2 (x - 3) = 1 \Rightarrow x - 3 = \frac{1}{2} \Rightarrow x = \frac{7}{2} \\ \Rightarrow y = \frac{1}{4} \end{array}$

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