11.3 The Tangent Line Problem. Spring 2011. At the end of this lesson, you should be able to. Use a tangent line to approximate the slope of a graph at a point. Use the limit definition of slope to find exact slopes of graphs.
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The tangent line to a graph of a function f at a point is the line that …
To determine the rate at which a graph rises or falls at a single point, ….
We can calculate the slope of a line given two points
Calculate the slope of the line between the given point P (5, 4) and another point on the curve, say Q(2, 1). The line is called a secant line.
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( , )
The slope mof the graph of f(x) at the point (x, f(x))
is equal to the slope of its tangent line at (x, f(x)),
and is given by
provided this limit exists.
Why do you think the slope of is a constant number? Explain.
The derivative is the formula which gives the slope of the tangent line at any point x for f(x)
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