$f\left(x\right)=x+\frac{1}{x}$ ফাংশনটির গুরু মান কত?

f(x)=x+x1​

To minimize f(x), we can take the derivative of f(x) with respect to x and set it equal to 0:

f′(x)=1−x21​=0

Now, solve for x:

1−x21​=0

1=x21​

x2=1

Taking the square root of both sides:

x=±1

So, the critical points are x=1 and x=−1.

Now, we need to determine which of these critical points corresponds to a minimum value of -2 for the function f(x). We can plug them back into the original function:

For x=1: f(1)=1+11​=1+1=2

For x=−1: f(−1)=−1+−11​=−1−1=−2

So, the minimum value of -2 is achieved when x=−1. Therefore, the function f(x)=x+x1​ has a minimum value of -2 at x=−1.