Given that the graph of $f$ passes through the point $( 4,69 )$ and that the slope of its tangent line at $( x , f ( x ) )$ is $11 x - 3$, find $f ( 1 )$. Select the correct answer.
A) $- 4.5$
B) 8
C) 12
D) 11
E) 1

Question

Quizplus · Accepted Answer

The slope of the tangent line at $( x , f ( x ) )$ is $11 x - 3$. So, $f'(x) = 11x - 3$. Integrating both sides, we get $f(x) = \frac{11}{2}x^2 - 3x + C$. Since the graph of $f$ passes through the point $( 4,69 )$, we have $69 = \frac{11}{2}(4)^2 - 3(4) + C$. Solving for $C$, we get $C = 1$. Therefore, $f(x) = \frac{11}{2}x^2 - 3x + 1$. So, $f(1) = \frac{11}{2}(1)^2 - 3(1) + 1 = - 4.5$.

Given That the Graph Of fff Passes Through the Point (4,69)( 4,69 )(4,69)

Given That the Graph Of $f$ Passes Through the Point $( 4,69 )$