EXAMPLE 10 Show that there is a root of the equation 2x3 − 4x2 + 3x − 2 = 0 between 1 and 2. SOLUTION Let f(x) = 2x3 − 4x2 + 3x − 2 = 0. We are looking for a solution of the given equation, that is, a number c between 1 and 2 such that f(c) = . Therefore we take a = , b = , and N = in the Intermediate Value Theorem. We have

Step-by-step explanation:

First, it is needed to determined the values for x = 1 and x = 2:

The sign change within the interval is the most sound evidence of the root existence. According to the Intermediate Value Theorem, there is a number such that . Another finding is that is closer to 1 than to 2.

i used to know how to do this in 7th but i forget easily

step-by-step explanation:

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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