46. Find a function y=f(x) whose second derivative is
y" = 12x - 2 at each point (x, y) on its graph and
y=- x+5 is tangent to the graph at the point corresponding to x = 1 .

Question

46. Find a function y=f(x) whose second derivative is
y" = 12x - 2 at each point (x, y) on its graph and
y=- x+5 is tangent to the graph at the point corresponding to x = 1 .

anonymous · Answer

we know 
$f'(x)=6x^2-2x+C$ 
lets see if we can find $C$

anonymous · Answer

if $y=-x+5$ is tangent to the curve at $x=1$ we know that $f'(1)=-1$ since the slope of $y=-x+5$ is $-1$ and since $f'(1)$ is that slope

setting $f'(1)=6-2+C=-1$ we can solve for $C$

anonymous · Answer

i get $C=-5$, making $f'(x)=6x^2-2x-5$

anonymous · Answer

this makes $f(x)=2x^3-x^2-5x+C$ and we have another constant to find.  
but $f(x)$ must agree with $y=-x+5$ at $x=1$ so replace $x$ by 1 in both $f(x)$ and $y$ and solve for $C$