In Exercises 37 and 38 , we specify a line by giving the slope and one point on the line. We give the first coordinate of some points on the line. Without deriving the equation of the line, find the second coordinate of each point. Slope is 2 , ( 1 , 3 ) on line; ( 2 , ) ; ( 3 , ) ; ( 0 , ) .
In Exercises 37 and 38 , we specify a line by giving the slope and one point on the line. We give the first coordinate of some points on the line. Without deriving the equation of the line, find the second coordinate of each point. Slope is 2 , ( 1 , 3 ) on line; ( 2 , ) ; ( 3 , ) ; ( 0 , ) .
Solution Summary: The author explains how to calculate the second coordinate of each of the points , whose slope is 2 and passes through the point . Substituting all the above values in the slope formula.
In Exercises
37
and
38
, we specify a line by giving the slope and one point on the line. We give the first coordinate of some points on the line. Without deriving the equation of the line, find the second coordinate of each point.
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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