Question

the max value of 10x -5x^2 -1 is
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Answer 1

given,

$y= 10x - 5x^2 - 1. \\dy/dx = 0 \\= (10 -10x - 1) x\\= 1. 10(1)-5(1)^2-1. \\=10-5-1. \\=4$

Answer 2

SOLUTION

TO DETERMINE

The maximum value of 10x - 5x² - 1

EVALUATION

Here the given expression is

10x - 5x² - 1

Now

$\sf{ = 10x - 5 {x}^{2} - 1}$

$\sf{ = - 5 {x}^{2} + 10x - 1}$

$\sf{ = - 5( {x}^{2} - 2x) - 1}$

$\sf{ = - 5( {x}^{2} - 2x + 1) + 5- 1}$

$\sf{ = - 5 {(x - 1)}^{2} + 4}$

$\sf{ = 4- 5 {(x - 1)}^{2} }$

Now the given expression is maximum when ( x - 1)² is minimum

We know that minimum value ( x - 1)² is 0

Hence the required maximum value of the expression

= 4 - 0

= 4

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