Find the equation of the function whose derivative is $f ^ { \prime } ( x ) = \frac { x ^ { 2 } + 9 x + 7 } { x - 1 }$ and whose graph passes through the point $( 2,4 )$ .
A) $\frac { x ^ { 2 } } { 2 } + 10 x + 17 \ln | x - 1 | - 19$
B) $\frac { x ^ { 2 } } { 2 } + 9 x + 17 \ln | x - 1 | - 18$
C) $\frac { x ^ { 2 } } { 2 } + 10 x + 17 \ln | x - 1 | - 18$
D) $\frac { x ^ { 2 } } { 2 } + 9 x + 7 \ln | x - 1 | - 18$
E) $\frac { x ^ { 2 } } { 2 } + 10 x + 7 \ln | x - 1 | - 19$

Question

Quizplus · Accepted Answer

To find the function, integrate the derivative $f'(x) = \frac{x^2 + 9x + 7}{x - 1}$. This results in $\frac{x^2}{2} + 10x + 17 \ln |x - 1| + C$. Using the point (2,4) to solve for C, we find $C = -18$. Thus, the function is $\frac{x^2}{2} + 10x + 17 \ln |x - 1| - 18$.

Find the Equation of the Function Whose Derivative Is f′(x)=x2+9x+7x−1f ^ { \prime } ( x ) = \frac { x ^ { 2 } + 9 x + 7 } { x - 1 }f′(x)=x−1x2+9x+7​

Find the Equation of the Function Whose Derivative Is $f ^ { \prime } ( x ) = \frac { x ^ { 2 } + 9 x + 7 } { x - 1 }$