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(a)
The function is .
Observe the graph .
Find the slope of the tangent line.
Slope of a tangent line with points and : .
Consider two points on the tangent line as and .
Slope of tangent line with points and and : .
Slope of the tangent line to the curve is .
(b)
The function is .
Observe the graph .
Find the slope of the tangent line.
Slope of a tangent line with points and : .
Consider two points on the tangent line as and .
Slope of tangent line with points and and : .
Slope of the tangent line to the curve is .
Verification:
(a)
The function is .
Find the slope of the tangent line.
Slope of the tangent line is the derivative of the function at a particular point.
Apply derivative on each side with respect to .
Apply power rule of derivatives: .
Substitute in the .
Slope of the curve is .
Slope of the tangent line to the curve is .
Verification:
(b)
The function is .
Find the slope of the tangent line.
Slope of the tangent line is the derivative of the function at a particular point.
Apply derivative on each side with respect to .
Apply power rule of derivatives: .
Substitute in the .
Slope of the curve is .
Slope of the tangent line to the curve is .
(a) Slope of the tangent line to the curve is .
(b) Slope of the tangent line to the curve is .
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