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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.
