The derivative of the function f is defined by f^(')(x)=x^(2)cos(3x). If f(6)=-6, then use a calculator to find the value of f(2) to the nearest thousandth. Answer:

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The derivative of the function  f is defined by  f^(')(x)=x^(2)cos(3x). If  f(6)=-6, then use a calculator to find the value of  f(2) to the nearest thousandth. Answer:

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Integrate f'(x) for f(x): To find the value of f(2), we need to integrate the derivative f'(x) to get the original function f(x). We will then use the initial condition f(6) = -6 to find the constant of integration.Use Symbolic Integration: The integral of f'(x) = x^2cos(3x) is a bit complex and typically requires integration by parts or a special technique. However, since we are not given the exact method for integration and are asked to use a calculator, we will assume that we can use a calculator that can handle symbolic integration.Apply Initial Condition: Using a calculator with symbolic integration capability, we integrate f'(x) to find f(x). The antiderivative of x^2cos(3x) is not straightforward, but we can write it as: f(x) = ∫x^2cos(3x) dx + C, where C is the constant of integration.Calculate Definite Integral: We apply the initial condition f(6) = -6 to solve for C. We substitute x = 6 into the integrated function and set it equal to -6: -6 = f(6) = ∫x^2cos(3x) dx from 0 to 6 + C. We calculate the definite integral from 0 to 6 and then solve for C.Find Constant C: After calculating the definite integral from 0 to 6, we find the value of C by solving the equation for C. Let's assume the calculator gives us the value of the integral, and we find C accordingly.Evaluate f(2: Now that we have the constant C, we can find f(2) by evaluating the antiderivative at x = 2 and adding the constant C: f(2) = ∫x^2cos(3x) dx from 0 to 2 + C. We calculate the definite integral from 0 to 2 using the calculator and then add the constant C to find f(2).Round to Nearest Thousandth: We round the result to the nearest thousandth as requested.

The derivative of the function $f$ is defined by $f^{\prime}(x)=x^{2} \cos (3 x)$ . If $f(6)=-6$ , then use a calculator to find the value of $f(2)$ to the nearest thousandth. $\newline$ Answer:

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The derivative of the function f f f is defined by f′(x)=x2cos⁡(3x) f^{\prime}(x)=x^{2} \cos (3 x) f′(x)=x2cos(3x). If f(6)=−6 f(6)=-6 f(6)=−6, then use a calculator to find the value of f(2) f(2) f(2) to the nearest thousandth.\newlineAnswer:

The derivative of the function $f$ is defined by $f^{\prime}(x)=x^{2} \cos (3 x)$ . If $f(6)=-6$ , then use a calculator to find the value of $f(2)$ to the nearest thousandth. $\newline$ Answer: