Intermediate+Value+Theorem

Intermediate Value Theorem

__**This theorem states that if f(x) is a continuos function, then on the interval [a,b] with a value of c between a and b then there is at least one number for x. in other words, f(x)=c **__

Examples:

Here try these Questions! #1  The graph h(x) is shown above. what is true about h(x): >> a) 1 and 3 b)2 only c)1,2and3 d)2 and 3 e)none are correct The correct answer is d) 2 and 3 because the entire graph is not continuous but certain sections are. Between x=-1 and x=2 the graph is continuous so it follows the Intermediate Value Theorem. At x=3 the graph is not continuous so it does not fulfill the Intermediate Value Theorem.
 * 1) h(x) is continuous on the interval [1,5]
 * 2) h(x) does NOT follow the Intermediate Value Theorem for the interval of [1,5]
 * 3) On the interval[-1,2] h(x) satisfies the Intermediate Value Theorem


 * 1) 2 Show that there is a y value of 0 on the intergal of [-2,1] for the equation f(x)= [[image:http://latex.codecogs.com/gif.latex?4x%5E%7B3%7D-3x+3]]

Solution: Input x values into equation to solve for y values. The value for x=-2 is -35 and the value for x=1 is 4. The graph is continuos so due to the Intermediate Value Theorem a value of y=0 has to occur

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