Question

For which values of a is the following function strictly increasing? (Posting function below)

Answer 1

\[f(x)= x^3 - ax^2+2x\]

Answer 2

\[f'(x)=3x ^{2}-2ax+2=3\left( x ^{2}-\frac{ 2a }{3}x+\frac{ a ^{2} }{9 }-\frac{ a ^{2} }{9 }\right)+2\]
\[=3\left( x-\frac{ a }{ 3 } \right)^{2}-3*\frac{ a ^{2} }{9 }+2\]
for strictly increasing function f'(x)>0
\[\frac{ -a ^{2} }{3 }+2>0,-a ^{2}>-6,a ^{2}<6,\left| a \right|<\sqrt{6},-\sqrt{6}<a<\sqrt{6}\]

Answer 3

so what about a=-sqrt(6) ? the f is still increasing in R\{-sqrt(6)/3}

Answer 4

or even other values of a
f is still strictly monotonous in parts of its domain

Answer 5

it is also there . we have to start at the end points.

Answer 6

strictly increasing*

Answer 7

I think f is strictly increasing for all values of a; it's just that it's strictly increasing for different parts of its domain.

(Just wanted to see how you guys would approach this one, i think the question should be written more specific)