Jackson rides his bike from his home for 30 minutes at a fast pace. He stops to rest for 20 minutes, and then continues riding i
1 answer:
Answer:
For the first 30 minutes, we will have a line with a given steepness, this will represent the 30 minutes riding at a fast pace.
Then he stops for 20 minutes, we will represent this with a constant line.
Then he again moves for another 30 minutes, but with a slower pace than in the first 30 minutes, then this line will be less steep than the first line.
A sketch of this situation can be seen below.
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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.