Question

Using the Intermediate Value Theorem, show that the function f has a zero between a and b. f(x)=x^3+4x^2-8x-10 a=-6, b=-5 What is f(-6)? What is f(-5)? Is there a zero between x= -6 and x= -5?

Answer 1

f(-6) means you substitute in -6 any time you see x in the function.

f(-5) means you substitute in -5 any time you see x in the function.

Evaluate for both those values and then compare the values.

If one is positive and one is negative, what must the graph of the function do between those two points?

Answer 2

i keep getting -13992 for the first one and that doesn't look right

Answer 3

(-6)^3 = -6 x -6 x -6 = -216

4*(-6)^2 = 4 * 36 = 144

8(-6) = -48

-216 + 144 - (-48) - 10 = -34

Answer 4

(-5)^3 = -5 * -5 * -5 = -125

4*(-5)^2 = 4 * 25 = 100

8(-5) = -40

-125 + 100 - (-40) - 10 = 5

Answer 5

So the ordered pairs of these two points are

(-6, -34) and (-5, 5)

To connect these two points, what must be true of the graph? Does it cross the x-axis?

Answer 6

oh, i was doing my multiplication wrong! and how would i determine whether or not it crosses the x axis?

Answer 7

If it goes from a negative y value to a positive y value, wouldn't it HAVE to cross the x-axis?