Question

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Find f(x) if f'(x) =7/x4 and f(1) = 4 (x4 x in üstü 4 yani)

Answer 1

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Given:-

• $f'(x) = \frac{7}{ {x}^{4} }$
• $f(1) = 4$

To Find:-

• $f(x)$

Solution:-

We start by integrating both sides.

$f(x) = \int \frac{7}{ {x}^{4} } dx$

$=>f(x) = 7\int {x}^{ - 4} dx$

$=>f(x) = 7 ( \frac{ {x}^{ - 4 + 1} }{ - 4 + 1}) + c$

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

$=>f(1) = 4 = 7( \frac{ {1}^{ - 3} }{ - 3} ) + c$

$=> \frac{7}{3} + c = 4$

$=>c = 4 - \frac{7}{3}$

$=>c = \frac{12}{3} - \frac{7}{3}$

$=>c = \frac{12 - 7}{3}$

$= > c = \frac{5}{3}$

Answer 2

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