What is the maximum value of 4(x + 7)(2 - x), over all real numbers x?

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

= 0

Or, = 0

Or, - 8 x - 20 = 0

Or, - 8 x = 20

∴  x =

i.e  x =

Now, Putting the value of x in the given equation

y = - 4 ( )² - 20 ( ) + 56

Or, y = - 4 () + 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

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