Find the maximum point of the following function:

$f\left( x \right) =-{ 3x }^{ 2 }+6x+1$

*
Check out the set:
2016 Problems
*

$\left( 1,3 \right)$
$\left( 3,5 \right)$
$\left( 1,4 \right)$
$\left( 2,5 \right)$

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

To find the maximum point, take the first derivative of the function then equate it to zero

$y = -3x^2 + 6x + 1$

$y' = -6x + 6$

Equate the first derivative to $0$ .

$-6x + 6 = 0$

$6x = 6$

$x = 1$

Now solve for $y$

$y = -3x^2 + 6x + 1$

$y = -3 + 6 + 1 = 4$