For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x -intercept(s). d. Determine the y -intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) f x = 5 x 2 − 15 x + 3
For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x -intercept(s). d. Determine the y -intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) f x = 5 x 2 − 15 x + 3
Solution Summary: The author explains how to determine whether the graph of the parabola opens upwards or downwards for the function.
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Elementary Statistics: Picturing the World (7th Edition)
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