The point P with the coordinates (3,m) lies on the curve y=x^2 + kx. At P the gradient of the curve is 8. Find the values of the constants k and m.

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unanimoose · Answer

The answer lies within your heart.

anonymous · Answer

Thanks?

anonymous · Answer

The point P with the coordinates (3,m) lies on the curve y=x^2 + kx. At P the gradient of the curve is 8. Find the values of the constants k and m.

Knowing that $(3,m)$ is a point on the curve is the same as knowing that when $x=3$, you have $y=m$. So you have one equation:
$$m=3^2+3k=9+3k$$
The gradient of the curve at this point (when $x=3$) is the value of the derivative at this point, which is given to be 8. So, you also know that
$$\frac{dy}{dx}=2x+k~~\implies~~8=6+k$$
You can directly solve for $k$ above, then use it to find the value of $m$.