With what values of parameter a the function f(x)=1/3x^3+a/2x^2+ax is really growing?
Answer: 0≤a≤4
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My solution so far:
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f'(x)=x^2+ax+a
Zero points of derivation:
x^2+ax+a=0
x=(-a±sqrt(a^2-4a))/2



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Zero points of derivation: assuming f'(x)=x^2+ax+a
x^2+ax+a=0			|-x²
ax+a=-x²			| (since x² will always be postive we can get the root now) sqrt(-x²)
x=sqrt(ax+a)