SOLUTION: determine the critical numbers and the critical points for each of the following functions:show all work A)f(x)= x3 + 3x2 -33x -35 B) g(x)=x3 - 36x C) h(x)= x3 -3x2 -40x

Algebra ->  Test -> SOLUTION: determine the critical numbers and the critical points for each of the following functions:show all work A)f(x)= x3 + 3x2 -33x -35 B) g(x)=x3 - 36x C) h(x)= x3 -3x2 -40x      Log On


   

Question 63932: determine the critical numbers and the critical points for each of the following functions:show all work

A)f(x)= x3 + 3x2 -33x -35
B) g(x)=x3 - 36x
C) h(x)= x3 -3x2 -40x
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
determine the critical numbers and the critical points for each of the following functions:show all work

A)f(x)= x^3 + 3x^2 -33x -35
f'(x)=3x^2+6x-33
0=3%28x%5E2%2B2x-11%29
0%2F3=3%28x%5E2%2B2x-11%29%2F3
0=x%5E2%2B2x-11 We can't solve this by factoring, so use the quadratic formula: x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
a=1, b=2, c=-11
x=%28-2%2B-sqrt%28%282%29%5E2-4%281%29%28-11%29%29%29%2F%282%281%29%29
x=%28-2%2B-sqrt%284%2B44%29%29%2F2
x=%28-2%2B-sqrt%2848%29%29%2F2
x=%28-2%2B-sqrt%2816%29%2Asqrt%283%29%29%2F2
x=%28-2-4%2Asqrt%283%29%29%2F2 and x=-2%2B4%2Asqrt%283%29%29%2F2
x=-1-2%2Asqrt%283%29 and x=1%2B2%2Asqrt%283%29
:
B) g(x)=x^3 - 36x
g'(x)=3x^2-36
0=3x%5E2-36
0%2B36=3x%5E2-36%2B36
36=3x%5E2
36%2F3=3x%5E2%2F3
12=x%5E2
+\-sqrt%2812%29=sqrt%28x%5E2%29
+\-sqrt%284%29%2Asqrt%283%29=x
+\-2%2Asqrt%283%29=x
:
C) h(x)= x^3 -3x^2 -40x
h'(x)=3x^2-6x-40
0=3x^2-6x-40 use the quadratic formula again.
a=3, b=-6, and c=-40
x=%28-%28-6%29%2B-sqrt%28%28-6%29%5E2-4%283%29%28-40%29%29%29%2F%282%283%29%29
x=%286%2B-sqrt%2836%2B480%29%29%2F6
x=%286%2B-sqrt%28516%29%29%2F6
x=%286%2B-sqrt%284%29%2Asqrt%28129%29%29%2F6
x=%286-2%2Asqrt%28129%29%29%2F6 and x=%286%2B2%2Asqrt%28129%29%29%2F6
x=2%283-sqrt%28129%29%29%2F%282%2A3%29 and x=2%283%2Bsqrt%28129%29%29%2F%282%2A3%29
x=%283-sqrt%28129%29%29%2F3 and x=%283%2Bsqrt%28129%29%29%2F3
:
Happy Calculating!!!