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Grade: upto college level
         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 s y = 2x2 and the slope of tangent is tanθ = dy/dx= 4x.

X 1 2 3 4 5 6 7 8 9 10
Y 2 8 18 32 50 72 98 128 162 200
5 years ago

Answers : (1)

Navjyot Kalra
askIITians Faculty
654 Points
							
Sol. The graph y = 2x2 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 line to meet
x-axis. Then find tan θ as shown in the figure.

It can be checked that,

Slope = tan θ = dy/dx = d/dx (2x2) = 4x 
Where x = the x-coordinate of the point where the slope is to be measured.

						
5 years ago
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