Suppose that g(t)=24te^kt for t> 0,where k is some constant.Find an appropriate value of k .
That makes more sense
We need to find g'(3) in other words and for a horizontal line g'(x) = 0
Use the product rule and the chain rule on g(t)
Spoiler:
$\displaystyle g'(t) = 24e^{kt}(1+kt)$
$\displaystyle g'(3) = 24e^{3k}(1+3k) = 0$
In $\displaystyle \mathbb{R}$ $\displaystyle 24e^{3k} > 0$ so it provides no solutions so $\displaystyle 1+3k = 0$ which gives $\displaystyle k = -\frac{1}{3}$