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AP® Calculus AB-BC

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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

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

C

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

D

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