For a certain automobile,
7.8m(x)=−.015x² +1.21x−7.8,
30≤x≤60,
represents the miles per gallon obtained at a speed of x miles per hour.

(a) find the absolute maximum miles per gallon and the speed at which it occurs.

(b) find the absolute minimum miles per gallon and the speed at which it occurs.

The answer is

a) 2,128 miles per gallon at 40,36 miles per hour

b) 1,388 miles per gallon at 60 miles per hour

Step-by-step explanation:

Let's find the extreme points of M(x) for 30≤x≤60. M(x) simplified by dividing to 7.8.

To find extreme points we find tangent of M(x) and equal it to 0.

therefore x=

This divides our x to 2 different range 30≤x≤40,36 and 40,36≤x≤60

Now we pick a number and investigate from the ranges

30≤x≤40,36   →    x = 35    →    M'(35) = 0,0206 which is > 0 and that means M is increasing

40,36≤x≤60   →    x = 45   →    M'(45) = -0,0178 which is < 0 and that means M is decreasing

Next let's look at critical points

   x                  M(x)          Before              After             Decision

  30                1,922              -                       ↑             Local Minimum Point

  40,36           2,128             ↑                       ↓             Local Maximum Point

  60                1,388             ↓                       -              Local Minimum Point

As we can see (30, 1,922) and (60, 1,388) are local minimum points and (40,36 , 2,128) is the local maximum point.

Since (60 , 1,388) is the lowest local minimum point it is the absolute minimum point and (40,36 , 2,128) is the absolute maximum point.

step-by-step explanation:

i hate black

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺