Question

Find the equation of the curve that passes through the point (3, 4) if its slope is given by
{dy}/{dx} = 7 x - 7.

Answer 1

Hello there :)
\[\Large\rm y'=7x-7\]The slope equation refers to the `derivative function`.

Answer 2

So in order to find the function, \(\Large\rm y\), we need to find an anti-derivative.
Do you know how to do that?

Answer 3

yeah it's \[(7x^2/2)-7x\]

Answer 4

More generally it is:\[\Large\rm y=\frac{7}{2}x^2-7x+c\]The c is very important.

Answer 5

Then plug in your given point, \(\Large\rm (3,4)\), and solve for c!