Physics In Exercises 67 – 70, (a) use the position equation s = − 16 t 2 + v 0 t + s 0 to write a function that represents the situation, (b) use a graphing utility to graph the function, (c) find the average rate of change of the function from t 1 to t 2 , (d) describe the slope of the secant line through t 1 and t 2 , (e) find the equation of the secant line through t 1 and t 2 , and (f) graph the secant line in the same viewing window as your position function. An object is thrown upward from a height of 6.5 feet at a velocity of 72 feet per second. t 1 = 0 , t 2 = 4
Physics In Exercises 67 – 70, (a) use the position equation s = − 16 t 2 + v 0 t + s 0 to write a function that represents the situation, (b) use a graphing utility to graph the function, (c) find the average rate of change of the function from t 1 to t 2 , (d) describe the slope of the secant line through t 1 and t 2 , (e) find the equation of the secant line through t 1 and t 2 , and (f) graph the secant line in the same viewing window as your position function. An object is thrown upward from a height of 6.5 feet at a velocity of 72 feet per second. t 1 = 0 , t 2 = 4
Solution Summary: The author explains how to graph the function s=-16t2+72t+6.5 by using graphing utility.
Physics In Exercises 67 – 70, (a) use the position equation
s
=
−
16
t
2
+
v
0
t
+
s
0
to write a function that represents the situation, (b) use a graphing utility to graph the function, (c) find the average rate of change of the function from
t
1
to
t
2
, (d) describe the slope of the secant line through
t
1
and
t
2
, (e) find the equation of the secant line through
t
1
and
t
2
, and (f) graph the secant line in the same viewing window as your position function.
An object is thrown upward from a height of 6.5 feet at a velocity of 72 feet per second.
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).
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