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nignag [31]
3 years ago
8

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

Mathematics
2 answers:
evablogger [386]3 years ago
6 0

Answer:

x = 1/2

Step-by-step 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

timurjin [86]3 years ago
5 0

Answer:

x = \frac{1}{2}

Step-by-step 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^{'} = \frac{dy}{dx} = \frac{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 = \frac{1}{2}

Therefore, the value of x for which the function is maximum is \frac{1}{2}

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