Find the greatest value of `f(x)=(1)/(2ax-x^(2)-5a^(2))` in [-3, 5] depending upon the parameter a.

Options

A. f(5) if a =1
B. f(-3) if a =1
C. f(5) if a `lt`1
D. f(-3) if a `gt` 1

Answer

1,2,3,4

Explanation

`f(x)=(1)/(2ax-x^(2)-5a^(2))=(1)/(-4a^(2)-(x-a)^(2)`

The graph is symmetrical about the line x =0 M
If a =1 (mid point of x =-5) greatest value is f(x) =f(-3)
If `alt1 f_(max)(x)=f(x5)=(-1)/(5a^(2)=2a+5)`
and if `agt1f_(max)(x)=f(-3)=(-1)/(5a^(2)+56a+9)`