Question

Исследуйте функцию с помощью производной y=3-x³+1

Answer 1

Воттттттт как то так

Answer 2

Exploring the Function with Derivative

To explore the function \( y = 3 - x^3 + 1 \) using the derivative, we can start by finding the derivative of the function with respect to \( x \).

The given function is: \[ y = 3 - x^3 + 1 \]

Finding the Derivative

The derivative of the function \( y = 3 - x^3 + 1 \) can be found using the power rule for differentiation. The power rule states that if \( f(x) = x^n \), then \( f'(x) = nx^{n-1} \).

Using the power rule, the derivative of the given function is: \[ y' = \frac{d}{dx}(3 - x^3 + 1) \]

\[ y' = -3x^2 \]

Conclusion

The derivative of the function \( y = 3 - x^3 + 1 \) with respect to \( x \) is \( y' = -3x^2 \).

This derivative represents the rate of change of the original function with respect to \( x \).