Answer:
Is ^5 on only x or on 5x ?
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When a negative number is multiplied by a negative number it becomes positive, but when a positive number is multiplied by a negative number it goes back to negative. -2 X -2 is 4, and 4 x -2 is -8. Hope this helped.
The first thing to do in this case is to replace the value of x = 60 in the given function to obtain the average fuel mileage in miles per gallon.
We then have to replace:
y = -0.0088 * x ^ 2 + 0.79 * x + 15
y = -0.0088 * (60) ^ 2 + 0.79 * (60) + 15
y = 30.7 mi / gal
answer
the best approximate for the average gas mileage at a speed of 60 miles per hour is
B) 30.7 mi / gal
A differentiable function 
is increasing on an open interval 
if 
for all 
, and decreasing if 
. For this problem, you then need to compute the derivative:
then solve for 
:
We can ignore 
because 
is defined only for 
. So we have two intervals to consider, 
and 
. All we need to do is pick any value from either interval and check the sign of the derivative 
. Since 
, from the first interval we can take 
, and from the second we can pick 
.
The above indicates that is decreasing on the first interval , and increasing on the second interval .
For part (b), we use the info from above as part of the first derivative test for extrema. We have one critical point at 
, and we know how behaves to either side of this point; decreases to left of it, and increases to the right. This pattern is indicative of a minimum occurring at , and we find that has the (local) minimum value of 
.
Let’s start with the easy part: half of the base is 3.
Therefore, 3 x h + 1 = 18
3 x h = 3h and 3 x 1 = 3
3h + 3 = 18
To solve these equations, you have to do the inverse. First you would need to minus 3:
3h = 15
3h is a simpler way of saying 3 x h, so the inverse would be a divide.
h = 5
