SOLUTION: determine the critical numbers and the critical points for each of the following functions A. f(x)= x^3 + 13x^2 + 7x - 165 B. g(x)= X^3 +6x^2 - 13x - 42 C. h(x)= x^3-10x^2

Algebra ->  Algebra  -> Functions -> SOLUTION: determine the critical numbers and the critical points for each of the following functions A. f(x)= x^3 + 13x^2 + 7x - 165 B. g(x)= X^3 +6x^2 - 13x - 42 C. h(x)= x^3-10x^2      Log On

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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
B. g(x)= X^3 +6x^2 - 13x - 42
C. h(x)= x^3-10x^2 + 7x + 18
THESE PROBLEMS ARE TOUGH....I REALLY NEED HELP WITH THEM...I TRIED DOING THEM BUT THE ANSWERS AREN'T RIGHT BECAUSE I KNOW THERE ARE SUPPOSED TO BE 2 ANSWERS 4 EACH BUT IM NOT SURE HOW TO GET THE SECOND NUMBER...PLEASE HELP...THANK YOU

Answer by funmath(2873) 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
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=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a a=3, b=26, and c=7
x=%28-26%2B-sqrt%28%2826%29%5E2-4%283%29%287%29%29%29%2F%282%283%29%29
x=%28-26%2B-sqrt%28676-84%29%29%2F6
x=%28-26%2B-sqrt%28592%29%29%2F6
x=%28-26%2B-sqrt%2816%29%2Asqrt%2837%29%29%2F6
x=%28-26-4sqrt%2837%29%29%2F6 and x=%28-26%2B4sqrt%2837%29%29%2F6
x=2%28-13-2sqrt%2837%29%29%2F%282%283%29%29 and x=2%28-13%2B2sqrt%2837%29%29%2F%282%283%29%29
x=%28-13-2sqrt%2837%29%29%2F3 and x=%28-13%2B2sqrt%2837%29%29%2F3
:
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=%28-12%2B-sqrt%28%2812%29%5E2-4%283%29%28-13%29%29%29%2F%282%283%29%29
x=%28-12%2B-sqrt%28144%2B156%29%29%2F%282%283%29%29
x=%28-12%2B-sqrt%28300%29%29%2F%282%283%29%29
x=%28-12%2B-sqrt%28100%29%2Asqrt%283%29%29%2F%282%283%29%29
x=%28-12-10sqrt%283%29%29%2F%282%283%29%29 and x=%28-12%2B10sqrt%283%29%29%2F%282%283%29%29
x=2%28-6-5sqrt%283%29%29%2F%282%283%29%29 and x=2%28-6%2B5sqrt%283%29%29%2F%282%283%29%29
x=%28-6-5sqrt%283%29%29%2F3 and x=%28-6%2B5sqrt%283%29%29%2F3
:
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=%28-%28-20%29%2B-sqrt%28%28-20%29%5E2-4%283%29%287%29%29%29%2F%282%283%29%29
x=%2820%2B-sqrt%28400-84%29%29%2F%282%283%29%29
x=%2820%2B-sqrt%28316%29%29%2F%282%283%29%29
x=%2820%2B-sqrt%284%29%2Asqrt%2879%29%29%2F%282%283%29%29
x=%2820-2sqrt%2879%29%29%2F%282%283%29%29 or x=%2820%2B2sqrt%2879%29%29%2F%282%283%29%29
x=2%2810-sqrt%2879%29%29%2F%282%283%29%29 or x=2%2810%2Bsqrt%2879%29%29%2F%282%283%29%29
x=%2810-sqrt%2879%29%29%2F3 or x=%2810%2Bsqrt%2879%29%29%2F3
Happy Calculating!!!