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Let

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).

 Nov 30, 2020
 #1
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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

 

 

cool cool cool

 Nov 30, 2020

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