Question

find the maximum value of y= -x^2+5x-25/4​

Answer 1

Answer:

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Answer 2

Answer:

The maximum value of $y= -x^2+5x-\frac{25}{4}$​ is 0.

Step-by-step explanation:

We are given $y=-x^2+5x-\frac{25}{4}$

Differentiate with respect to $x$ on both sides.

$\frac{dy}{dx} =-2x+5$ ----------(1)

put  $\frac{dy}{dx} =0$

$-2x+5=0$

$2x=5$

$x=\frac{5}{2}$

Differentiate (1) with respect to $x$.

$\frac{d^2y}{dx^2} =-2 < 0$  (negative)

So, maximum value exists at $x=\frac{5}{2}$.

Maximum value

Substitute x=5/2 in the given expression.

$-(\frac{5}{2} )^2+5(\frac{5}{2} )-\frac{25}{4}$

$(\frac{-25}{4} )+(\frac{25}{2} )-(\frac{25}{4} )$

On adding first and last term. We get,

$\frac{-25}{2} +\frac{25}{2}$

Perform subtraction. We get,

$=0$

Therefore, the maximum value exists  at x=5/2 is 0.