Find the point on the graph of the function $f ( x ) = ( x + 1 ) ^ { 2 }$ that is closest to the point $( - 5,1 )$ . Round all numerical values in your answer to four decimal places.
A) $( - 2.3918,1.9370 )$
B) $( 3.3811,1.9370 )$
C) $( 2.3918,1.9370 )$
D) $( - 1.937,3.3811 )$
E) $( - 3.3811,2.3918 )$

Question

Find the point on the graph of the function $f ( x ) = ( x + 1 ) ^ { 2 }$ that is closest to the point $( - 5,1 )$ . Round all numerical values in your answer to four decimal places. 
A) $( - 2.3918,1.9370 )$
B) $( 3.3811,1.9370 )$ 
C) $( 2.3918,1.9370 )$
D) $( - 1.937,3.3811 )$
E) $( - 3.3811,2.3918 )$

Quizplus · Accepted Answer

To find the point on the graph of $f(x) = (x + 1)^2$ closest to $(-5,1)$, we can use the distance formula between two points $(x, y)$ and $(-5, 1)$, where $y = f(x) = (x + 1)^2$. Minimizing this distance with respect to $x$ involves calculus, specifically taking the derivative of the distance squared (to avoid the square root) with respect to $x$, setting it to zero, and solving for $x$. This process yields $x = -2.3918$, and substituting this value back into $f(x)$ gives $y = 1.9370$, making the closest point $(-2.3918, 1.9370)$.

Find the Point on the Graph of the Function f(x)=(x+1)2f ( x ) = ( x + 1 ) ^ { 2 }f(x)=(x+1)2

Find the Point on the Graph of the Function $f ( x ) = ( x + 1 ) ^ { 2 }$