Sketch the graph of the function f(x) = √x and label the point (4, 2) on the graph. (a) Find the slope of the line joining (4, 2) and (9, 3). Is the slope of the tangent line at (4, 2) greater than or less than this number? (b) Find the slope of the line joining (4, 2) and (1, 1). Is the slope of the tangent line at (4, 2) greater than or less than this number? (c) Find the slope of the line joining (4, 2) and (4.41, 2.1). Is the slope of the tangent line at (4, 2) greater than or less than this number? (d) Find the slope of the line joining (4, 2) and (4 + h, f(4 + h)) in terms of the nonzero number h. (e) What is the slope of the tangent line at (4, 2)? Explain how you arrived at your answer.
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Sketch the graph of the function f(x) = √x and label the point (4, 2) on the graph. (a) Find the slope of the line joining (4, 2) and (9, 3). Is the slope of the tangent line at (4, 2) greater than or less than this number? (b) Find the slope of the line joining (4, 2) and (1, 1). Is the slope of the tangent line at (4, 2) greater than or less than this number? (c) Find the slope of the line joining (4, 2) and (4.41, 2.1). Is the slope of the tangent line at (4, 2) greater than or less than this number? (d) Find the slope of the line joining (4, 2) and (4 + h, f(4 + h)) in terms of the nonzero number h. (e) What is the slope of the tangent line at (4, 2)? Explain how you arrived at your answer.
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