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

Question

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

Bytelearn · Accepted Answer

Integrate f'(x): To find f(6), we need to integrate the derivative f'(x) to get the original function f(x). The integral of f'(x) = (x^2 - x)cos(x) will give us f(x) up to a constant C.Use calculator for integration: We integrate f'(x) = (x^2 - x)cos(x) using integration by parts or a calculator with symbolic integration capabilities. However, since the problem asks us to use a calculator, we will assume the use of a calculator for this step.Find constant C: After integrating, we get f(x) = ∫(x^2 - x)cos(x) dx + C, where C is the constant of integration. We need to find the value of C using the initial condition f(-3) = -6.Solve for C: We plug x = -3 into the integrated function to solve for C: f(-3) = ∫(-3^2 - (-3))cos(-3) dx + C = -6.Calculate definite integral: We use the calculator to find the definite integral from -3 to 6 of (x^2 - x)cos(x) dx. This will give us the change in f(x) from f(-3) to f(6).Apply Fundamental Theorem of Calculus: We add the result of the definite integral to the initial value f(-3) = -6 to find f(6). This is because the Fundamental Theorem of Calculus tells us that the definite integral from a to b of f'(x) dx is equal to f(b) - f(a).Find definite integral I: Using the calculator, we find the definite integral from -3 to 6 of (x^2 - x)cos(x) dx. Let's denote this value as I.Calculate f(6): We calculate f(6) = f(-3) + I = -6 + I.Round to nearest thousandth: We round the result to the nearest thousandth as the problem asks for the answer in that precision.

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

Full solution

More problems from Find the roots of factored polynomials

Related topics

The derivative of the function f f f is defined by f′(x)=(x2−x)cos⁡(x) f^{\prime}(x)=\left(x^{2}-x\right) \cos (x) f′(x)=(x2−x)cos(x). If f(−3)=−6 f(-3)=-6 f(−3)=−6, then use a calculator to find the value of f(6) f(6) f(6) to the nearest thousandth.\newlineAnswer:

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