SOLUTION: Using the intermediate value theorem, determine, if possible, whether the function f has at least one real zero between a and b. f(x)=x^(3)+4x^(2)-6x-13; a=-8, b=-4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Using the intermediate value theorem, determine, if possible, whether the function f has at least one real zero between a and b. f(x)=x^(3)+4x^(2)-6x-13; a=-8, b=-4      Log On


   

Question 1131288: Using the intermediate value theorem, determine, if possible, whether the function f has at least one real zero between a and b. f(x)=x^(3)+4x^(2)-6x-13; a=-8, b=-4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E%283%29%2B4x%5E%282%29-6x-13
a=-8, b=-4+
f%28-8%29=%28-8%29%5E%283%29%2B4%28-8%29%5E%282%29-6%28-8%29-13
f%28-8%29=-221}
f%28-4%29=%28-4%29%5E%283%29%2B4%28-4%29%5E%282%29-6%28-4%29-13
f%28-4%29=11
Now we know:
at x=-221, the curve is below zero
at x=11, the curve is above+zero
And, being a polynomial, the curve will be continuous, so somewhere in between the curve must cross through f%28x%29=0
Yes, there is a solution to x%5E%283%29%2B4x%5E%282%29-6x-13=+0 in the interval [-8, -4]

+graph%28+600%2C+600%2C+-15%2C+15%2C+-10%2C10%2C+x%5E%283%29%2B4x%5E%282%29-6x-13%29+