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# help

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

Jul 6, 2020

#1
+28021
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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
+10583
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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.

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

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

$$y_{max}=13.75$$

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

!

Jul 6, 2020
edited by asinus  Jul 6, 2020