Question

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

Answer 1

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 $\frac{1}{2}$

Answer 2

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