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Vitek1552 [10]
3 years ago
11

Find f if f ''(x) = 12x2 + 6x − 4, f(0) = 5, and f(1) = 4.

Mathematics
1 answer:
Taya2010 [7]3 years ago
6 0
This is a differential equations problem.  We are to work backwards and determine the function f(x) when given f "(x) and initial values.

<span>f ''(x) = 12x^2 + 6x − 4, when integrated with respect to x, yields:

                x^3        x^2
f '(x) = 12------ + 6----- - 4x + C, or 4x^3 + 3x^2 - 4x + C, and
                  3            2

             x^4         x^3        x^2
f(x) = 4------- + 3------- - 4------ + Cx + D, or f(x)=x^4 + x^3 - 2x^2 + Cx + D
               4              3         2

Now, because f(0)=5, 5=0^4 + 0^3 -2(0)^2 + C(0) + D, so that D=5.
Determine D in the same manner:  Let x=1 and find the value of C.

Then the solution, f(x), is x^4 + x^3 - 2x^2 + Cx + 5.  Replace C with this value and then you'll have the desired function f(x).</span>
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we believe that 42% of freshmen do not visit their counselors regularly. For this year, you would like to obtain a new sample to
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A sample of 1077 is required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

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The margin of error is of:

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A sample size of n is required, and n is found when M = 0.035. So

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0.035\sqrt{n} = 2.327\sqrt{0.42*0.58}

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