for f(x)=x^2+kx+k, determine all values of k such that f(x)>0
The minimum of f(x) occurs when
f'(x) = 2x + k = 0, x = -k/2
The value of f(x) at that minimum is
f(-k/2) = k^2/4 -k^2/2 +k = k^2/4 + k
That minimum is >0 if k>0 or k< -4
The minimum of f(x) occurs when
f'(x) = 2x + k = 0, x = -k/2
The value of f(x) at that minimum is
f(-k/2) = k^2/4 -k^2/2 +k = k^2/4 + k
That minimum is >0 if k>0 or k< -4
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