Question

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 draw is y = 2x² and the slope of tangent is \[\tan \theta = \frac{dy}{dx} = 4x\] 
\[\begin{array}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ y & 2 & 8 & 18 & 32 & 50 & 72 & 98 & 128 & 162 & 200\end{array}\]

Answer 1

Note: Students should draw the graph y = 2x² on a graph paper for results.

To find a slope at any point, draw a tangent at the point and extend the line to meet the x-axis. Then find tan θ as shown in the figure.

The above can be checked as follows:

\[Slope = \tan \theta = \frac{dy}{dx}\]

\[ = \frac{d}{dx}\left( 2 x^2 \right) = 4x\]
Here, x = x-coordinate of the point where the slope is to be measured.