Ishaan94 Group Title Is this function linear? $\sum_{k=1}^{n}\left(a - a_1\right)\cdot\left(a-a_2\right)\cdots\left(a-a_n\right)$ Where $$a_1,a_2, \ldots, a_n \in \left[0,a\right]$$. 2 years ago 2 years ago

1. Ishaan94

@mukushla

2. Ishaan94

$$a$$ is any positive integer.

3. Ishaan94

I need to determine maximum of the function

4. eliassaab

Linear with respect to a

5. eliassaab

?

6. Ishaan94

but I am confused a bit

7. eliassaab

This function does not seem to be linear.

8. Ishaan94

If it's linear it will be maximum at end points right?

9. Ishaan94

does not. hmm but in the book it says it is and i am confused.

10. mukushla

with respect to a not linear wrt to any of ai linear

11. Ishaan94

if some function were xy + y + x, would it still be linear? y and x are variables. or (a-y)(a-x).

12. Ishaan94

i am sorry if i am asking stupid questions, i am just confused

13. mukushla

for function xy + y + x if u fix y(for example) function will be linear wrt x