(a)
The meaning of slope of the tangent line.
(a)
Explanation of Solution
A tangent to a function
Tangent line is parallel to graph of function given in the problem.
So,
Slope of tangent line tells us the rate of change at a particular instant.
(b)
The comparison of slope of the tangent line to the slope of the secant line.
(b)
Explanation of Solution
Secant line is the line that touches the graph at a single point, that is not parallel to the graph of the function whereas tangent line is the line that touches the graph at a single point, that is parallel to graph of the function.
(c)
The meaning of normal line to a graph.
(c)
Explanation of Solution
Normal line is the line that is perpendicular to the tangent line to the graph of function given in the problem.
The slope of the normal line is the negative reciprocal of the slope of the tangent line.
A normal line can touch the graph of the function at more than one point.
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