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Find the value of x for which the function below is maximum

Find the value of x for which the function below is maximum-example-1
User Enzokie
by
7.9k points

2 Answers

1 vote

Answer:

x = 1/2

Explanation:

The standard equation of a quadratic function is given by:

y = ax² + bx + c, If a > 0 then the graph has a minimum but if a < 0, then the graph has a maximum. To find the maximum or minimum, we differentiate the function with respect to x and equate to zero that is y'(x) = 0.

For the function y = 5 + x - x², a = -1 < 0, therefore it has a maximum.

Differentiating with respect to x:

y'(x) = 1 - 2x

Equating to zero

-2x + 1 = 0

-2x = -1

x = -1/ -2

x = 1/2

The function has a maximum at x = 1/2

User RED MONKEY
by
8.3k points
6 votes

Answer:

x =
(1)/(2)

Explanation:

Given function;

y = 5 + x - x²

To find the maximum value, follow these steps

(i) Find the first derivative (which is the slope) of the given function with respect to x. i.e;


y^(') =
(dy)/(dx) =
(d(5 + x - x^2))/(dx)


y^(') =
1 - 2x

(ii) From the result in (i) determine the value of x for which the slope is zero. i.e.

x for which

1 - 2x = 0

=> 1 = 2x

=> x =
(1)/(2)

Therefore, the value of x for which the function is maximum is
(1)/(2)

User Stryku
by
7.8k points

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