Matrix M gives the manufacturer price for four models of dining room tables. Matrix P gives the retail price to the customer. Wood Metal M = $ 1050 $ 940 $ 890 $ 800 Large Small Wood Metal P = $ 1365 $ 1222 $ 1157 $ 1040 Large Small a. Compute P − M and interpret its meaning. b. if the tax rate in a certain city is 6 % , use scalar multiplication to find a matrix F that gives the final price (including sales tax) to the for each model.
Matrix M gives the manufacturer price for four models of dining room tables. Matrix P gives the retail price to the customer. Wood Metal M = $ 1050 $ 940 $ 890 $ 800 Large Small Wood Metal P = $ 1365 $ 1222 $ 1157 $ 1040 Large Small a. Compute P − M and interpret its meaning. b. if the tax rate in a certain city is 6 % , use scalar multiplication to find a matrix F that gives the final price (including sales tax) to the for each model.
Solution Summary: The author calculates the difference matrix P-M and interprets its meaning.
Matrix
M
gives the manufacturer price for four models of dining room tables. Matrix
P
gives the retail price to the customer.
Wood
Metal
M
=
$
1050
$
940
$
890
$
800
Large
Small
Wood
Metal
P
=
$
1365
$
1222
$
1157
$
1040
Large
Small
a. Compute
P
−
M
and interpret its meaning.
b. if the tax rate in a certain city is
6
%
, use scalar multiplication to find a matrix
F
that gives the final price (including sales tax) to the for each model.
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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