AP® Calculus AB-BC

Free Version

Upgrade subject to access all content

Difficult

Minimum Of $f(x)$

APCALC-WNDXRS

Given $f^{ \prime \prime }( x ) =4x-1$ and $f^{ \prime }( 0 ) =-1,$ at what point does $f(x)$ reach a minimum if $f(x)$ goes through the point $(0, 2)$?

A

$ (0, 2)$

B

$ \left(1, \cfrac{7}{6}\right)$

C

$ \left(1, -\cfrac{17}{6}\right)$

D

$ \left(-\cfrac{1}{2}, 0\right)$