Prove that the function f(x)=x^2+(a/x) cannot have a local maximum for any value of a.
Any help would be greatly appreciated thanks.
Hello, Sophia27!
We have: .Prove that the function cannot have a local maximum for any value of
Then: .
Multiply by . (critical value)
Second derivative: .
Then: .
At our critical value, the second derivative is positive; the graph is concave up,
We have one critical value and it is a local minimum.
Therefore, the function has no local maximum value.