8th Problem 2016

Algebra Level 2

Find the maximum point of the following function:

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

Check out the set: 2016 Problems

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

Angela Fajardo by Angela Fajardo , 19, Philippines

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1 solution

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

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

y ′ = − 6 x + 6 y' = -6x + 6

Equate the first derivative to 0 0 .

− 6 x + 6 = 0 -6x + 6 = 0

6 x = 6 6x = 6

x = 1 x = 1

Now solve for y y

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

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

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