a)
To find:the slope of the graph of the function at the indicated point using the limit of definition of the derivative.
The slope of the graph of the function at the point
Given information:
Formula used:
The derivative of the function
The derivative of a function at a point can be viewed geometrically as the slope of the line tangent to the curve
Calculation:
Calculate the derivative of the function
Calculate
Therefore,the slope of the graph of the function at the point
b)
To find: an equation of the tangent line at that point.
The equation of the tangent line at point
Given information:
Formula used:
Let
Calculation:
It is given that
Calculate
The tangent is passing through point
Compute the equation of the tangent line at point
Therefore, the equation of the tangent line at point
c)
To sketch:a graph of the curve near the point without using a grapher.
The graph is a parabola.
Given information:
Formula used:
The derivative of the function
The derivative of a function at a point can be viewed geometrically as the slope of the line tangent to the curve
Calculation:
Sketch the graph of
Prepare a table of points for
Plot the above points and connect them.
Therefore, it can be observed that the graph is a parabola.
Chapter 11 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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