Question

Find all critical points of the function f(x) = x^3 + 5x^2 - 7x - 3. If there is more than one critical point, list them in descending order and separate them by commas.The critical point(s) is(are) =

Answer 1

Given the following question:

`f\mleft(x\mright)=x^3+5x^2-7x-3`
`\begin{gathered} f(x)=x^(3)+5x^(2)-7x-3 \\ x^3=3x^2 \\ x^2=2x \\ 5x*2x=10x \\ x=1 \\ 7x=7\left(1\right)=7*1=7 \\ 3x^2+10x-7 \\ \text{ To find the critical points} \\ 3x^2+10x-7=0 \\ -(5)/(3)+(√(46))/(3) \\ -(√(46))/(3)-(5)/(3) \\ \text{ The critical points are:} \\ -(5-√(46))/(3),(484-92√(46))/(27) \\ -(5+√(46))/(3),(484+92√(46))/(27) \\ \end{gathered}`