The derivative of the function f is defined by f^(')(x)=(x^(2)+3)sin(2x). If f(4)=7, then use a calculator to find the value of f(-1) to the nearest thousandth. Answer:

Integrate f'(x): To find the value of f(-1), we need to integrate the derivative f'(x) to get the original function f(x). We will then use the initial condition f(4) = 7 to find the constant of integration.Use initial condition: First, we integrate f'(x) = (x^2 + 3)sin(2x). This requires integration by parts or a special technique since it is a product of a polynomial and a trigonometric function. However, we cannot directly integrate this without more information or a different approach because the problem asks for the value of f(-1) and not the general form of f(x).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The derivative of the function
f is defined by
f^(')(x)=(x^(2)+3)sin(2x). If
f(4)=7, then use a calculator to find the value of
f(-1) to the nearest thousandth.
Answer:

The derivative of the function $f$ is defined by $f^{\prime}(x)=\left(x^{2}+3\right) \sin (2 x)$ . If $f(4)=7$ , then use a calculator to find the value of $f(-1)$ to the nearest thousandth. $\newline$ Answer:

View step-by-step help

Home

Math Problems

Grade 8

Evaluate variable expressions for sequences

Full solution

Q. The derivative of the function

f

is defined by

f^{\prime}(x)=\left(x^{2}+3\right) \sin (2 x)

. If

f(4)=7

, then use a calculator to find the value of

f(-1)

to the nearest thousandth.

\newline

Answer:

Integrate $f'(x)$ : To find the value of $f(-1)$ , we need to integrate the derivative $f'(x)$ to get the original function $f(x)$ . We will then use the initial condition $f(4) = 7$ to find the constant of integration.
Use initial condition: First, we integrate $f'(x) = (x^2 + 3)\sin(2x)$ . This requires integration by parts or a special technique since it is a product of a polynomial and a trigonometric function. However, we cannot directly integrate this without more information or a different approach because the problem asks for the value of $f(-1)$ and not the general form of $f(x)$ .