Hey guys and gals.
I was wondering if I could get some help with a question that reads.
Determine the x-intercepts of the curve which has a slope 2x +1 and passes through (1, -4)
Thank You so much!
If it has a slope of $\displaystyle 2x + 1$ then we can say
$\displaystyle \frac{dy}{dx} = 2x + 1$.
Therefore
$\displaystyle y = \int{2x + 1\,dx}$
$\displaystyle y = x^2 + x + C$.
We're told that $\displaystyle (1, -4)$ lies on the curve, so
$\displaystyle -4 = 1^2 + 1 + C$
$\displaystyle -4 = 1 + 1 + C$
$\displaystyle -4 = 2 + C$
$\displaystyle -6 = C$.
Thus $\displaystyle y = x^2 + x - 6$.