Question

при каких значениях p дробь принимает наибольшее значение (√ p-1)\(p - 1)

Answer 1

область определения р>1,

и на области определения функция монотонно убывет.

и не имеет экстремума.

Answer 2

Finding the Maximum Value of the Fraction (√p-1)/(p+1)

To find the values of p for which the fraction (√p-1)/(p+1) takes the maximum value, we can use calculus to find the critical points and determine the maximum value.

The first step is to find the derivative of the function (√p-1)/(p+1) with respect to p. Then, we can set the derivative equal to zero to find the critical points. Finally, we can use the second derivative test to determine whether these critical points correspond to a maximum value.

Calculating the Derivative and Critical Points

The derivative of the function (√p-1)/(p+1) can be calculated using the quotient rule:

Derivative of f(p) = (√p-1)/(p+1)

The derivative is given by: ``` f'(p) = (p+1)*((1/2)*(p-1)^(-1/2)) - (√p-1)*(1)/(p+1)^2 ```

Setting the derivative equal to zero and solving for p will give us the critical points.

Determining the Maximum Value

After finding the critical points, we can use the second derivative test to determine whether these points correspond to a maximum value.

The second derivative of the function can be calculated to determine the concavity and confirm whether the critical points correspond to a maximum value.

By following these steps, we can find the values of p for which the fraction (√p-1)/(p+1) takes the maximum value.