## anonymous 4 years ago 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 $$a_1,a_2, \ldots, a_n \in \left[0,a\right]$$.

1. anonymous

@mukushla

2. anonymous

$$a$$ is any positive integer.

3. anonymous

I need to determine maximum of the function

4. anonymous

Linear with respect to a

5. anonymous

?

6. anonymous

but I am confused a bit

7. anonymous

This function does not seem to be linear.

8. anonymous

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

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

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

13. anonymous

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