Answer:
The maximum value of function is 81 .
Step-by-step explanation:
Given function as :
y = 4 (x + 7) (2 - x)
Now, The function can be written as
y = 4 (2 x - x² + 14 - 7 x)
y = 4 ( - x² - 5 x + 14)
y = - 4 x² - 20 x + 56
Now, For maximum value of function , differentiation of y with respect to x
[tex]\frac{\partial y}{\partial x}[/tex] = 0
Or, [tex]\frac{\partial ( - 4x^{2} - 20 x +56)}{\partial x}[/tex] = 0
Or, - 8 x - 20 = 0
Or, - 8 x = 20
∴ x = [tex]\dfrac{-20}{8}[/tex]
i.e x = [tex]\dfrac{-5}{2}[/tex]
Now, Putting the value of x in the given equation
y = - 4 ( [tex]\dfrac{-5}{2}[/tex])² - 20 ( [tex]\dfrac{-5}{2}[/tex]) + 56
Or, y = - 4 ([tex]\dfrac{25}{4}[/tex]) + 50 + 56
Or, y = - 25 + 50 + 56
∴ y = 81
So, The maximum value of function is 81
Hence,The maximum value of function is 81 . Answer
