The ratio of boys to girls in Ella’s grade is 3 to 4. The ratio of boys to girls in Minh’s grade is 4 to 5. Each grade has a tot
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Just add the displacement value to variable. If this value is positive, the graph will move to the right, otherwise it will shift to left.
Where: x=displacement value
If you notice any mistake in my English, please let me know, because I am not native.
Where: x=displacement value
If you notice any mistake in my English, please let me know, because I am not native.
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.