f^(')(x)=-(4)/(x^(2)) and f(2)=4. f(1)=

Find Derivative of f(x): We know the derivative of f(x), which is f'(x) = -(4)/(x^(2)). We need to find f(1).Use Derivative to Find Rate of Change: Since we have f(2) = 4, we can use the derivative to find the rate of change of the function, but we can't directly find f(1) from f'(x) without integrating.Integrate f'(x) to Find f(x): Let's integrate f'(x) to get f(x). The integral of f'(x) = -(4)/(x^(2)) is f(x) = 4/x + C, where C is the constant of integration.Find Constant C: We can find the constant C by using the given point f(2) = 4. Plugging in the values, we get 4 = 4/2 + C, which simplifies to 4 = 2 + C.Calculate f(1): Solving for C, we get C = 4 - 2, which is C = 2.Now we have the function f(x) = 4/x + 2. We can find f(1) by plugging in x = 1.f(1) = 4/1 + 2, which simplifies to f(1) = 4 + 2.So, f(1) = 6.

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f^(')(x)=-(4)/(x^(2)) and
f(2)=4.

f(1)=

$f^{\prime}(x)=-\frac{4}{x^{2}}$ and $f(2)=4$ . $\newline$ $f(1)=$

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f^{\prime}(x)=-\frac{4}{x^{2}}

and

f(2)=4

\newline

f(1)=

Find Derivative of $f(x)$ : We know the derivative of $f(x)$ , which is $f'(x) = -\frac{4}{x^{2}}$ . We need to find $f(1)$ .
Use Derivative to Find Rate of Change: Since we have $f(2) = 4$ , we can use the derivative to find the rate of change of the function, but we can't directly find $f(1)$ from $f'(x)$ without integrating.
Integrate $f'(x)$ to Find $f(x)$ : Let's integrate $f'(x)$ to get $f(x)$ . The integral of $f'(x) = -\frac{4}{x^{2}}$ is $f(x) = \frac{4}{x} + C$ , where $C$ is the constant of integration.
Find Constant C: We can find the constant C by using the given point $f(2) = 4$ . Plugging in the values, we get $4 = \frac{4}{2} + C$ , which simplifies to $4 = 2 + C$ .
Calculate $f(1)$ : Solving for $C$ , we get $C = 4 - 2$ , which is $C = 2$ .
Calculate $f(1)$ : Solving for $C$ , we get $C = 4 - 2$ , which is $C = 2$ .Now we have the function $f(x) = \frac{4}{x} + 2$ . We can find $f(1)$ by plugging in $x = 1$ .
Calculate $f(1)$ : Solving for $C$ , we get $C = 4 - 2$ , which is $C = 2$ .Now we have the function $f(x) = \frac{4}{x} + 2$ . We can find $f(1)$ by plugging in $x = 1$ . $f(1) = \frac{4}{1} + 2$ , which simplifies to $f(1) = 4 + 2$ .
Calculate $f(1)$ : Solving for $C$ , we get $C = 4 - 2$ , which is $C = 2$ .Now we have the function $f(x) = \frac{4}{x} + 2$ . We can find $f(1)$ by plugging in $x = 1$ . $f(1) = \frac{4}{1} + 2$ , which simplifies to $f(1) = 4 + 2$ .So, $f(1) = 6$ .