Mr. Parker has driven 55 miles of a 300-mile trip. If he is traveling at or below the 70 miles per hour speed limit, how much lo
nger can Mr. Parker expect the trip to last?
A tennis racquet costs $43.75 and a can of tennis balls costs $3.25. How many cans of tennis balls can you buy along with a tennis racquet and be under your $60.00 budget
An annual pass to the local zoo is $40.00. The daily pass is $12.00. What is the least number of times you can visit the zoo with the annual pass to make it the better deal?
A tennis racquet costs $43.75 and a can of tennis balls costs $3.25. How many cans of tennis balls can you buy along with a tennis racquet and be under your $60.00 budget
An annual pass to the local zoo is $40.00. The daily pass is $12.00. What is the least number of times you can visit the zoo with the annual pass to make it the better deal?
2 answers:
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Answer with explanation:
Let us assume that the 2 functions are:
1) f(x)
2) g(x)
Now by definition of concave function we have the first derivative of the function should be strictly decreasing thus for the above 2 function we conclude that
Now the sum of the 2 functions is shown below
Diffrentiating both sides with respect to 'x' we get
Since each term in the right of the above equation is negative thus we conclude that their sum is also negative thus
Thus the sum of the 2 functions is also a concave function.
Part 2)
The product of the 2 functions is shown below
Diffrentiating both sides with respect to 'x' we get
Now we can see the sign of the terms on the right hand side depend on the signs of the function's themselves hence we remain inconclusive about the sign of the product as a whole. Thus the product can be concave or convex.