The derivative of the function f is defined by f^(')(x)=x^(3)sin(x). If f(4)=-7, then use a calculator to find the value of f(0) to the nearest thousandth. Answer:

Integrate f'(x): Integrate f'(x) = x^3sin(x) to find f(x).Find Constant of Integration: Use the given information f(4) = -7 to find the constant of integration.Calculate Integral from 0 to 4: Calculate the integral of f'(x) from 0 to 4 using a calculator.Solve for f(0): Set the result of the integral equal to f(4) + f(0) and solve for f(0).Find Value of I: Use the calculator to find the value of I, the integral from 0 to 4 of f'(x).Substitute into f(0): Substitute the value of I into the equation f(0) = -7 - I and find f(0).Round to Nearest Thousandth: Round the value of f(0) to the nearest thousandth.

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The derivative of the function
f is defined by
f^(')(x)=x^(3)sin(x). If
f(4)=-7, then use a calculator to find the value of
f(0) to the nearest thousandth.
Answer:

The derivative of the function $f$ is defined by $f^{\prime}(x)=x^{3} \sin (x)$ . If $f(4)=-7$ , then use a calculator to find the value of $f(0)$ to the nearest thousandth. $\newline$ Answer:

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Algebra 2

Find trigonometric ratios using multiple identities

Full solution

Q. The derivative of the function

f

is defined by

f^{\prime}(x)=x^{3} \sin (x)

. If

f(4)=-7

, then use a calculator to find the value of

f(0)

to the nearest thousandth.

\newline

Answer:

Integrate $f'(x)$ : Integrate $f'(x) = x^3\sin(x)$ to find $f(x)$ .
Find Constant of Integration: Use the given information $f(4) = -7$ to find the constant of integration.
Calculate Integral from $0$ to $4$ : Calculate the integral of $f'(x)$ from $0$ to $4$ using a calculator.
Solve for $f(0)$ : Set the result of the integral equal to $f(4) + f(0)$ and solve for $f(0)$ .
Find Value of I: Use the calculator to find the value of $I$ , the integral from $0$ to $4$ of $f'(x)$ .
Substitute into $f(0)$ : Substitute the value of $I$ into the equation $f(0) = -7 - I$ and find $f(0)$ .
Round to Nearest Thousandth: Round the value of $f(0)$ to the nearest thousandth.