Draw a graph from the following data. Draw tangents at $x = 2, 4, 6$ and $8$ . Find the slopes of these tangents. Verify that the curve drawn is $y = 2 x^{2}$ and the slope of tangent is $tan θ = \frac{d y}{d x} = 4 x$ .
x $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$
$10$
y $2$ $8$ $18$ $32$ $50$ $72$ $98$ $128$ $162$ $200$

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Solution

The graph $y = 2 x^{2}$ should be drawn by the student on a graph paper for exact results.
To find slope at any point, draw a tangent at the point and extend the lne to meet x=axis. Then find $tan θ$ as shown in the figure.
It can be checked that,
Slope $= tan θ = \frac{d y}{d x} = \frac{d}{d x} (2 x^{2}) = 4 x$ .
where $x =$ the x-coordinate of the point where the slope is to be measured.

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x	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
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Draw a graph from the following data. Draw tangents at x=2,4,6 and 8. Find the slopes of these tangents. Verify that the curve drawn is y=2x2 and the slope of tangent is tanθ=dydx=4x.x12345678910y281832507298128162200