let \(g\) be the function given by \(g(x)=x^3e^{kx}\), where \(k\) is a constant. For what value of \(k\) does \(g\) have a critical point at \(x=\dfrac{1}{2}\) ?
let \(g\) be the function given by \(g(x)=x^3e^{kx}\), where \(k\) is a constant. For what value of \(k\) does \(g\) have a critical point at \(x=\dfrac{1}{2}\) ?