Question 63961
determine the critical numbers and the critical points for each of the following functions

A. f(x)= x^3 + 13x^2 + 7x - 165
f'(x)=3x^2+26x+7
0=3x^2+26x+7  
Use the quadratic formula:
{{{x=(-b+-sqrt(b^2-4ac))/2a}}} a=3, b=26, and c=7
{{{x=(-26+-sqrt((26)^2-4(3)(7)))/(2(3))}}}
{{{x=(-26+-sqrt(676-84))/6}}}
{{{x=(-26+-sqrt(592))/6}}}
{{{x=(-26+-sqrt(16)*sqrt(37))/6}}}
{{{x=(-26-4sqrt(37))/6}}} and {{{x=(-26+4sqrt(37))/6}}}
{{{x=2(-13-2sqrt(37))/(2(3))}}} and {{{x=2(-13+2sqrt(37))/(2(3))}}}
{{{x=(-13-2sqrt(37))/3}}} and {{{x=(-13+2sqrt(37))/3}}}
:
B. g(x)= X^3 +6x^2 - 13x - 42
g'(x)=3x^2+12x-13
0=3x^2+12x-13
Use the quadratic formula, a=3, b=12, and c=-13
{{{x=(-12+-sqrt((12)^2-4(3)(-13)))/(2(3))}}}
{{{x=(-12+-sqrt(144+156))/(2(3))}}}
{{{x=(-12+-sqrt(300))/(2(3))}}}
{{{x=(-12+-sqrt(100)*sqrt(3))/(2(3))}}}
{{{x=(-12-10sqrt(3))/(2(3))}}} and {{{x=(-12+10sqrt(3))/(2(3))}}}
{{{x=2(-6-5sqrt(3))/(2(3))}}} and {{{x=2(-6+5sqrt(3))/(2(3))}}}
{{{x=(-6-5sqrt(3))/3}}} and {{{x=(-6+5sqrt(3))/3}}}
:
C. h(x)= x^3-10x^2 + 7x + 18
h'(x)=3x^2-20x+7
0=3x^2-20x+7
Use the quadratic formula a=3, b=-20, and c=7
{{{x=(-(-20)+-sqrt((-20)^2-4(3)(7)))/(2(3))}}}
{{{x=(20+-sqrt(400-84))/(2(3))}}}
{{{x=(20+-sqrt(316))/(2(3))}}}
{{{x=(20+-sqrt(4)*sqrt(79))/(2(3))}}}
{{{x=(20-2sqrt(79))/(2(3))}}} or {{{x=(20+2sqrt(79))/(2(3))}}}
{{{x=2(10-sqrt(79))/(2(3))}}} or {{{x=2(10+sqrt(79))/(2(3))}}}
{{{x=(10-sqrt(79))/3}}} or {{{x=(10+sqrt(79))/3}}}
Happy Calculating!!!