Find a function 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

Start by integrating y'' twice to get function y(x).



Next find value of coefficients 'c' and 'd' using the given tangent line
The slope of tangent line is equal to y' when x=1.



The tangent line intersects the curve y(x) when x = 1.
If x = 1, then y = 4  (From y =-x+5)



Final