Answer:
a. The critcal points are at
b. Then, 
is a maximum and 
is a minimum
c. The absolute minimum is at 
and the absolute maximum is at 
Step-by-step explanation:
(a)
Remember that you need to find the points where
Therefore you have to solve this equation.
From that equation you can factor out 
and you would get
And from that you would have 
, so 
.
And you would also have 
.
You can factor that equation as 
Therefore 
.
So the critcal points are at
b.
Remember that a function has a maximum at a critical point if the second derivative at that point is negative. Since
Then, is a maximum and is a minimum
c.
The absolute minimum is at and the absolute maximum is at
The same would be the right one
Answer:
14.4 km/h
Step-by-step explanation:
When finding km/h given m/s always multiply by 3.6
When finding m/s given km/h do the vice versa (divide by 3.6)
So.. 4km/h x 3.6 = <u>14.4 km/h </u>
Answer:
The watch is cheaper in Geneva, Switzerland by a value of £20
Step-by-step explanation:
To get the city in which the watch is cheaper, what we need to do is to express the price of the watch in the same currency.
Since pounds is also used in the b part of the question, it would be easier working with it.
In Geneva, the price of the watch is 193.75 CHF
from our conversion formula;
£1 = 1.55 CHF
£x = 193.75 CHF
We cross multiply to get the value of x
(193.75 * 1)/1.55
= 193.75/1.55 = £125
We can see that the watch costs less in Geneva and higher in Manchester
By how much is it cheaper?
We can calculate this by subtracting the value in Geneva from the value in Manchester
That would be 145-125 = £20 cheaper
Answer:
The number of complex roots is 6.
Step-by-step explanation:
Descartes's rule of signs tells you that the number of positive real roots is 0. The number of negative real roots will be at most 2. The minimum value of the left side will be between x=0 and x=-1, but will never be negative. Thus all six roots are complex.
_____
The magnitude of x^3 will exceed the magnitude of x^6 only for values of x between -1 and 1. Since the magnitude of either of these terms will not be more than 1 in that range, the left-side expression must be positive everywhere.
