Given:
[tex]4x^3-18x^2-48x-3[/tex]find: critical number of point of a function.
Explanation: critical numbers are values of a function where the function's tangent lines.
[tex]\begin{gathered} y=4x^3-18x^2-48x-3 \\ \frac{dy}{dx}=12x^2-36x-48=0 \\ x^2-3x-4=0 \\ x^2-(4-1)x-4=0 \\ x^2-4x+x-4=0 \\ x(x-4)+(x-4)=0 \\ (x-4)(x+1)=0 \\ x=4,-1 \end{gathered}[/tex]Final answer: there are two critical number x=4 and -1.
