If h(x) = x – 7 and g(x) = x2, which expression is equivalent to(g*h)(5)? a (5 – 7)2, b (5)2 – 7, c (5)2(5 – 7), d (5 – 7)x2
1 answer:
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A) 
is continuous, so 
is also continuous. This means if we were to integrate 
, the same constant of integration would apply across its entire domain. Over 
, we have 
. This means that
For to be continuous, we need the limit as 
to match 
. This means we must have
Now, over
, we have 
, so 
, which means 
.
b) Integrating over [1, 3] is easy; it's just the area of a 2x2 square. So,
c) is increasing when 
, and concave upward when 
, i.e. when is also increasing.
We have
over the intervals 
and 
. We can additionally see that 
only on and .
d) Inflection points occur when
, and at such a point, to either side the sign of the second derivative 
changes. We see this happening at 
, for which 
, and to the left of we have decreasing, then increasing along the other side.
We also have along the interval 
, but even if we were to allow an entire interval as a "site of inflection", we can see that to either side, so concavity would not change.
For
Now, over
b) Integrating over [1, 3] is easy; it's just the area of a 2x2 square. So,
c)
We have
d) Inflection points occur when
We also have
Answer:
Step-by-step explanation:
(a) Given
Sam charge $5 for each dog for a thirty minute walk
For an hour which is double the thirty minutes, it must be double of the same charge.
(b)Given
With $20, Christie sells 100 cups of lemonade with a quarter per cup charge
For 100 cup, she generate a revenue of
So, she earns that is , her profit is