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Find the maximum value of the function f(x) = -3x^2 + 9x + 7.

 Jul 6, 2020
 #1
avatar+28021 
+1

This is a dome shaped parabola due to the   negative leading coefficient

 

the 'x' value of the vertex will be found by   - b/2a     where b = 9   and a =-3

 

use this value of 'x' in the equation to find the 'y' value of the vertex which will be the function's maximum value.....

 Jul 6, 2020
 #2
avatar+10583 
+2

Find the maximum value of the function f(x) = -3x^2 + 9x + 7.

 

Hello Guest!

 

The extremes of a function are at the zeros of the 1st derivative of the function.

 

\(f(x) = -3x^2 + 9x + 7\\ \frac{df(x)}{dx}=-6x+9=0\\ x_{max}=1,5\)

\(y = -3x^2 + 9x + 7\\ y=-3\cdot 1.5^2+9\cdot 1.5+7\)

\(y_{max}=13.75\)

 

\(P_{max}(1.5,\ 13.75)\)

laugh  !

 Jul 6, 2020
edited by asinus  Jul 6, 2020

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