f(x) = 5x^2 + 6 if x <= a
f(x) = 11x if x > a
Find the smallest possible value for a if the graph of y = f(x) is continuous (which means the graph can be drawn without lifting your pencil from the paper).
Yo find "a" just set the equations equal
5x^2 + 6 = 11x rearramge as
5x^2 - 11x + 6 = 0 actor
(5x - 6) ( x - 1) = 0
The smallest x = "a" will occur when
x - 1 = 0
x = 1 = "a"
See the graph here : https://www.desmos.com/calculator/ryznv6php2