The Force $\ { F }$ (In Newtons) of a Hydraulic Cylinder in a Press Is

Multiple Choice

The Force $\ { F }$ (in newtons) of a hydraulic cylinder in a press is proportional to the square of $\sec x$ where $x$ is the distance (in meters) that the cylinder is extended in its cycle. The domain of $F$ is $\left[ 0 , \frac { \pi } { 3 } \right]$ and $F ( 0 ) = 150$ . Find $F$ as a function of $x$ .

A) $F ( x ) = 150 \sec ^ { 2 } x$
B) $F ( x ) = 150 + \sec ^ { 2 } x$
C) $F ( x ) = 300 \sec ^ { 2 } x$
D) $F ( x ) = \sec ^ { 2 } x + 1$
E) $F ( x ) = 75 \sec ^ { 2 } x$