Find the coordinates of the maximum point on the curve y = -2xsquared + 6x + 3. Explain how you know it is a maximum?

f'(x) = -4 x + 6

so maximum point is when f'(x) = 0 so

-4x + 6 = 0

-4 x = -6

x = 1.5

Sustituing we get

y = 7.5

so (1.5, 7.5) is this correct?

How can I garanty it being the maximum point though?