Question

Find the equation of the curve having y’ = 2x – 5 that passes through (5,4). 

Answer 1

Let us find the equation of the curve having $y' = 2x – 5$ that passes through $(5,4).$ It follows that $y=x^2-5x+C,$ and hence $4=5^2-5^2+C=C.$ We conclude that the equation of the curve is $y=x^2-5x+4.$