Question

if x be real,find the maximum value of 7+10x-5x^2.

Answer 1

1. One method is to differentiate the expression
f(X) = 7+10x-5x²
Differentiating , we get, f'(x) = 10- 10x
Equating it to 0, (10-10x=0), we get x=1
Substituting this value (x=1) in the given expression, we get,
f(1) = 7+10-5 = 12



2. Other method is to make the expression a function of a perfect square
$7 + 10x - 5 {x}^{2} \\ = 7 + 5 - 5 + 10x - 5 {x}^{2} \\ = 12 - 5( {x}^{2} - 2x + 1) \\ = 12 - 5( {x - 1)}^{2}$
Observe that the maximum value of -5(x-1)² is when (x-1) is 0 (or when x= 1)

:.The maximum avoid of the given expression is :
12-0
= 12

Hope this helps!!!
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Answer 2

Answer:

12

Step-by-step explanation:

The method and the answer of the other person who answered this is already correct :)