f^(')(x)=-(50)/(x^(3)) and f(1)=20. f(5)=

Derivative Calculation: We have the derivative f'(x) = -(50)/(x^3). To find f(5), we need to integrate f'(x) from 1 to 5.Antiderivative Calculation: The antiderivative of f'(x) is f(x) = -(50)/(2x^2) + C, where C is the constant of integration.Constant of Integration: We know f(1) = 20, so plug in x = 1 to find C: 20 = -(50)/(2*1^2) + C.Finding f(5): Simplify to find C: 20 = -25 + C, so C = 20 + 25, C = 45.Simplification: Now we have f(x) = -(50)/(2x^2) + 45. Plug in x = 5 to find f(5): f(5) = -(50)/(2*5^2) + 45.Final Result: Simplify the expression: f(5) = -(50)/(2*25) + 45, f(5) = -(50)/50 + 45, f(5) = -1 + 45.Final calculation: f(5) = 44.

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f^(')(x)=-(50)/(x^(3)) and
f(1)=20.

f(5)=

$f^{\prime}(x)=-\frac{50}{x^{3}}$ and $f(1)=20$ . $\newline$ $f(5)=$

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Precalculus

Operations with rational exponents

Full solution

f^{\prime}(x)=-\frac{50}{x^{3}}

and

f(1)=20

\newline

f(5)=

Derivative Calculation: We have the derivative $f'(x) = -\frac{50}{x^3}$ . To find $f(5)$ , we need to integrate $f'(x)$ from $1$ to $5$ .
Antiderivative Calculation: The antiderivative of $f'(x)$ is $f(x) = -\frac{50}{2x^2} + C$ , where $C$ is the constant of integration.
Constant of Integration: We know $f(1) = 20$ , so plug in $x = 1$ to find $C$ : $20 = -\frac{50}{2 \cdot 1^2} + C$ .
Finding $f(5)$ : Simplify to find $C$ : $20 = -25 + C$ , so $C = 20 + 25$ , $C = 45$ .
Simplification: Now we have $f(x) = -\frac{50}{2x^2} + 45$ . Plug in $x = 5$ to find $f(5)$ : $f(5) = -\frac{50}{2\cdot5^2} + 45$ .
Final Result: Simplify the expression: $f(5) = -\frac{50}{2\times 25} + 45$ , $f(5) = -\frac{50}{50} + 45$ , $f(5) = -1 + 45$ .
Final Result: Simplify the expression: $f(5) = -\frac{50}{2\cdot 25} + 45$ , $f(5) = -\frac{50}{50} + 45$ , $f(5) = -1 + 45$ . Final calculation: $f(5) = 44$ .