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(a) .
Approximate a tangent line to the given curve at the point .
Slope of the tangent line is the derivative of the function.
Draw the tangent line at .
Observe the graph.
The tangent line passes through the points and .
Slope of the tangent line at is .
(b) .
Approximate a tangent line to the given curve at the point .
Slope of the tangent line is the derivative of the function.
Draw the tangent line at .
Observe the graph.
Since the tangent line is horizontal, .
Slope of the tangent line at is .
(c) .
Approximate a tangent line to the given curve at the point .
Slope of the tangent line is the derivative of the function.
Draw the tangent line at .
Observe the graph.
The tangent line passes through the points and .
Slope of the tangent line at is .
(d) .
Approximate a tangent line to the given curve at the point .
Slope of the tangent line is the derivative of the function.
Draw the tangent line at .
Observe the graph.
The tangent line passes through the points and .
Slope of the tangent line at is .
(e) .
Approximate a tangent line to the given curve at the point .
Slope of the tangent line is the derivative of the function.
Draw the tangent line at .
Observe the graph.
The tangent line passes through the points and .
Slope of the tangent line at is .
(f) .
Approximate a tangent line to the given curve at the point .
Slope of the tangent line is the derivative of the function.
Draw the tangent line at .
Observe the graph.
Since the tangent line is horizontal, .
Slope of the tangent line at is .
(g) .
Approximate a tangent line to the given curve at the point .
Slope of the tangent line is the derivative of the function.
Draw the tangent line at .
Observe the graph.
The tangent line passes through the points and .
Slope of the tangent line at is .
Make table for the slopes of these lines for given values of x :
Graph :
1) Draw the co-ordinate plane.
2) Plot the points obtained in the above table.
3) Connect the points with a smooth curve.
Graph of differential function is :
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Graph of differential function is :
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