For what value of k the function f(x)=kx3+5 is decreasing.

Dear Student,

Please find below the solution to the asked query:
$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)={\mathrm{kx}}^3+5 \\ {\mathrm{f}}^{\text{'}}\left(\mathrm{x}\right)=3{\mathrm{kx}}^2 \\ \mathrm{f}\left(\mathrm{x}\right) \mathrm{is} \mathrm{decreasing} \mathrm{So} \\ {\mathrm{f}}^{\text{'}}\left(\mathrm{x}\right)<0 \\ 3{\mathrm{kx}}^2<0 \\ \mathrm{k}<0 \\ \mathrm{Answer} \end{gathered}$$

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