Answer:
The equation of the line that goes through points (1,1) and (3,7) is 
Step-by-step explanation:
Determine the equation of the line that goes through points (1,1) and (3,7)
We can write the equation of line in slope-intercept form  where m is slope and b is y-intercept.
 where m is slope and b is y-intercept.
We need to find slope and y-intercept.
Finding Slope
Slope can be found using formula: 
We have 
Putting values and finding slope

We get Slope = 3
Finding y-intercept
y-intercept can be found using point (1,1) and slope m = 3

We get y-intercept b = -2
So, equation of line having slope m=3 and y-intercept b = -2 is:

The equation of the line that goes through points (1,1) and (3,7) is 
 
        
             
        
        
        
Coefficient of x is less than 0 then it's across the y axis
So f(x)=2^x ---> g(x) = 2^-x
Then translating it up 5 units, should be  g(x) = 2^(-x)  + 5
Answer is the last one
g(x) = 2^(-x) + 5
 
        
                    
             
        
        
        
Per 1,000 units the last one
        
                    
             
        
        
        
The Lagrangian,

has critical points where its partial derivatives vanish:





 tells us
 tells us  , so that
, so that


Then with  , we get
, we get

and  tells us
 tells us

Then there are two critical points,  . The critical point with the negative
. The critical point with the negative  -coordinates gives the maximum value,
-coordinates gives the maximum value,  .
.