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

Question

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

Bytelearn · Accepted Answer

Integrate f'(x) for f(x): To find f(-2), we need to integrate f'(x) to get f(x) and then use the initial condition f(3) = -4 to find the constant of integration.Non-standard integral: The integral of f'(x) is the integral of (x^3 + 3x)cos(3x + 4). This requires integration by parts or a substitution method. However, this is a non-standard integral that does not have a simple antiderivative, so we cannot proceed with this step directly.Numerical integration approximation: Since we cannot find an explicit form for f(x), we will use numerical methods to approximate the value of f(-2). We can use numerical integration techniques to approximate the integral of f'(x) from 3 to -2.Perform numerical integration: We will use a calculator to perform the numerical integration of f'(x) from 3 to -2. The result of this integration will give us the change in f(x) from f(3) to f(-2).Calculate f(-2): After performing the numerical integration, we add the result to the initial value f(3) = -4 to find f(-2). Let's assume the calculator gives us the value of the integral as I. Then f(-2) = f(3) + I.Unfortunately, without an actual calculator or numerical integration software, we cannot provide the numerical value of the integral I, and thus cannot provide the value of f(-2). This step requires the use of technology to complete.

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

Full solution

More problems from Find trigonometric ratios using multiple identities

Related topics

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