If f(x) = x^3 and g(x) = (x + 1)^3, which is the graph of g(x)?
1 answer:
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Answer:
The answer that gives the best estimate is (1,1)
Step-by-step explanation:
i) As can be seen on of the lines intercepts the y axis at (0,-1). So the y
intercept or = -1. Therefore the equation for this line can be written as
y = x +
⇒ y =
x - 1 . It can also be seen from this graph that the
line passes through the point (2 , 2). Substituting these values for x and y
respectively we get 2 = 2 - 1 ∴
=
. The equation of the first line
can be written as y = x - 1 ⇒ 2y - 3x = -2
ii) As can be seen on the other line the intercept on the y axis is at (0,2). So
the y intercept or = 2. Therefore the equation for this line can be
written as y = x +
⇒ y =
x + 2 . It can also be seen from this
graph that the line passes through the point (1 , -1). Substituting these
values for x and y respectively we get 1 = 1 + 2 ∴
= -1 . The
equation of the second line can be written as y = - x + 2 or x + y = 2
iii) Solving the two equations of the two lines respectively as found in i) and
ii) we get y = 0.8. We multiply equation in ii) by 3 to get 3x + 3y = 6 and
when we add this to equation in i) we get 5y = 4 which means that y = 0.8.
If we substitute this value in ii) we get 0.8 + x = 2 , therefore x = 1.2.
iv) Therefore we get the solution of the two lines, which is the intersection
of the two lines as (1.2, 0.8). So the answer that gives the best estimate
is (1,1)
Answer:
(a) fave = 8
(b) c = 64/9
(c) c ≈ 7.111
Step-by-step explanation:
(a) The average value of the function is its integral over the interval, divided by the width of the interval.
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(b) We want ...
f(c) = 8
3√c = 8 . . . . . use f(c)
√c = 8/3 . . . . . divide by 3
c = (8/3)² . . . . square
c = 64/9
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(c) c ≈ 7.111