Answer: you need to add a picture, otherwise we don’t know how to help you answer that questions
Step-by-step explanation:
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
![\frac{d}{dx}\cdot f(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Ccdot%20f%28x%29%3C0%5C%5C%5C%5C%5Cfrac%7Bd%7D%7Bdx%7D%5Ccdot%20g%28x%29%3C0)
Now the sum of the 2 functions is shown below
![y=f(x)+g(x)](https://tex.z-dn.net/?f=y%3Df%28x%29%2Bg%28x%29)
Diffrentiating both sides with respect to 'x' we get
![\frac{dy}{dx}=\frac{d}{dx}\cdot f(x)+\frac{d}{dx}\cdot g(x)\\\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7Bd%7D%7Bdx%7D%5Ccdot%20f%28x%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%5Ccdot%20g%28x%29%5C%5C%5C%5C)
Since each term in the right of the above equation is negative thus we conclude that their sum is also negative thus
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3C0)
Thus the sum of the 2 functions is also a concave function.
Part 2)
The product of the 2 functions is shown below
![h=f(x)\cdot g(x)](https://tex.z-dn.net/?f=h%3Df%28x%29%5Ccdot%20g%28x%29)
Diffrentiating both sides with respect to 'x' we get
![h'=\frac{d}{dx}\cdot (f(x)\cdot g(x))\\\\h'=g(x)f'(x)+f(x)g'(x)](https://tex.z-dn.net/?f=h%27%3D%5Cfrac%7Bd%7D%7Bdx%7D%5Ccdot%20%28f%28x%29%5Ccdot%20g%28x%29%29%5C%5C%5C%5Ch%27%3Dg%28x%29f%27%28x%29%2Bf%28x%29g%27%28x%29)
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.
Answer:
7 3/20
Step-by-step explanation:
I took the quiz.
Answer:
good morning I was just asking when will I be
Answer:
-3q² + 3qp + 2rp - 2rq + Sq - Sp
Step-by-step explanation:
first part
3q(p-q) = 3qp - 3q²
second part
2r(p-q) = 2rp - 2rq
third part
S(q-p) = Sq - Sp
then we put it all together
3qp - 3q² + 2rp - 2rq + Sq - Sp
in the right place possibly
-3q² + 3qp + 2rp - 2rq + Sq - Sp