# Math Help - Turning point of the curve

1. ## Turning point of the curve

The curve $y=hx^2+\frac{k}{x}$ has a turning point at $P(\frac{1}{2},6)$.Find

(i)the value of $h$ and $k$

(ii)the equation of tangent to the curve at $x=1$

2. Originally Posted by mastermin346
The curve $y=hx^2+\frac{k}{x}$ has a turning point at $P(\frac{1}{2},6)$.Find

(i)the value of $h$ and $k$

(ii)the equation of tangent to the curve at $x=1$
the point $P\left(\frac{1}{2} , 6 \right)$ is on the curve ...

$6 = \frac{h}{4} + 2k$

since $P$ is a turning point ...

$y'\left(\frac{1}{2}\right) = 0$

use the above equation to get a second equation in terms of $h$ and $k$ ... then solve the system of equations.