Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra
$f' (x) = 7 x^{2} + 8 x^{11} - 18; f (0) = - 2$

The antiderivative can be given as $f (x) = \frac{7}{3} x^{3} + \frac{8}{12} x^{12} - 18 x - 2$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 2: Given information

We are given the derivative as $f' (x) = 7 x^{2} + 8 x^{11} - 18; f (0) = - 2$

Step 2: Find the antiderivative

We know that differentiating a power function decreases the power by one we can start with the function $f (x) = x^{3} + x^{12} - 18 x + c$

On differentiating the function we get,

$f' (x) = 3 x^{2} + 12 x^{11} - 18$

which is nearly equal

Now we only adjust the coefficient

$f (x) = \frac{7}{3} x^{3} + \frac{8}{12} x^{12} - 18 x + c$

Also we are given $f (0) = - 2 S u b s t i t u t i n g t h i s i n t h e f u n c t i o n w e g e t, c = - 2$

Hence the antiderivative becomes

$f (x) = \frac{7}{3} x^{3} + \frac{8}{12} x^{12} - 18 x - 2$

Step 3: Conclusion

The antiderivative can be given as $f (x) = \frac{7}{3} x^{3} + \frac{8}{12} x^{12} - 18 x - 2$

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Calculus

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Short Answer

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra
$f' (x) = 7 x^{2} + 8 x^{11} - 18; f (0) = - 2$

Step by Step Solution

Step 2: Given information

Step 2: Find the antiderivative

Step 3: Conclusion

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Calculus

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Short Answer

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra f'(x)=7x2+8x11-18 ; f(0)=-2

Step by Step Solution

Step 2: Given information

Step 2: Find the antiderivative

Step 3: Conclusion

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Pure Maths

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra
$f' (x) = 7 x^{2} + 8 x^{11} - 18; f (0) = - 2$