What are the critical values of $f (x) = 3 x^{2} + 2 x + 5$ $f(x)=3x^2+2x+5$ ?

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Answer 1 · 2018-07-15T18:02:15

$x = - \frac{1}{3}, y = \frac{14}{3}$ $x=-1/3,y=14/3$

Computing the first derivative of $f (x)$ $f(x)$ we get

$f'(x)=6x+2$
solving the equation $f'(x)=0$
we get $x=-1/3$

since $f''(x)=6>0$ we get a minimum (this is global, since we have a parabola)
and we get

$f(-1/3)=3*1/9-2/3+5=(1-2+15)/3=14/3$

What are the critical values of f(x)=3x^2+2x+5f(x)=3x2+2x+5f(x)=3x^2+2x+5?