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Question

Draw a graph from the following data. Draw tangents at x = 2, 6 and 8. Find the slopes of these tangents. Verify that the curve draw is y = 2x2 and the slope of tangent is tan θ=dydx=4x.
x12345678910y281832507298128162200

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Solution

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 θ=dydx =ddx2x2=4x
Here, x = x-coordinate of the point where the slope is to be measured


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