The derivative of the function f is defined by f^(')(x)=(x^(3)+3x)cos(2x+5). If f(-3)=-5, then use a calculator to find the value of f(4) to the nearest thousandth. Answer:

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The derivative of the function  f is defined by  f^(')(x)=(x^(3)+3x)cos(2x+5). If  f(-3)=-5, then use a calculator to find the value of  f(4) to the nearest thousandth. Answer:

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Integrate f'(x) for f(x): To find f(4), we need to integrate the derivative f'(x) to get the original function f(x). The integral of f'(x) will give us f(x) up to a constant C, which we can determine using the given value f(-3) = -5.Complex Integral Calculation: The integral of f'(x) = (x^3 + 3x)cos(2x + 5) is not straightforward due to the product of a polynomial and a trigonometric function. We will need to use a numerical method or a calculator to approximate the integral from -3 to 4.Numerical Integration Process: Using a calculator with numerical integration capabilities, we input the function (x^3 + 3x)cos(2x + 5) and integrate from x = -3 to x = 4. This will give us the change in f(x) over this interval.Calculate f(4): After performing the numerical integration, we obtain a value (let's call it I). To find f(4), we use the fact that f(4) = f(-3) + I. Since we know f(-3) = -5, we can calculate f(4) = -5 + I.Substitute and Solve: We substitute the value of I obtained from the calculator into the equation f(4) = -5 + I to find the value of f(4) to the nearest thousandth.

The derivative of the function $f$ is defined by $f^{\prime}(x)=\left(x^{3}+3 x\right) \cos (2 x+5)$ . If $f(-3)=-5$ , then use a calculator to find the value of $f(4)$ to the nearest thousandth. $\newline$ Answer:

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The derivative of the function f f f is defined by f′(x)=(x3+3x)cos⁡(2x+5) f^{\prime}(x)=\left(x^{3}+3 x\right) \cos (2 x+5) f′(x)=(x3+3x)cos(2x+5). If f(−3)=−5 f(-3)=-5 f(−3)=−5, then use a calculator to find the value of f(4) f(4) f(4) to the nearest thousandth.\newlineAnswer:

The derivative of the function $f$ is defined by $f^{\prime}(x)=\left(x^{3}+3 x\right) \cos (2 x+5)$ . If $f(-3)=-5$ , then use a calculator to find the value of $f(4)$ to the nearest thousandth. $\newline$ Answer: