y = (x + 1)3
It looks like you have an equation \( y = (x + 1)^3 \). This is a cubic function. If you need help with a specific aspect of this function, such as finding its derivative, evaluating it for certain values, or graphing it, please let me know! Here are some general insights:
Expansion: You can expand \( (x + 1)^3 \) to get: \[ (x + 1)^3 = x^3 + 3x^2 + 3x + 1 \]
Derivative: The derivative \( \frac{dy}{dx} \) of this function can be calculated as follows: \[ \frac{dy}{dx} = 3(x + 1)^2 \] or using the expanded form: \[ \frac{dy}{dx} = 3x^2 + 6x + 3 \]
Intercepts:
- Y-intercept: Set \( x = 0 \): \[ y = (0 + 1)^3 = 1 \] So the y-intercept is at \( (0, 1) \).
- X-intercept: Set \( y = 0 \): \[ 0 = (x + 1)^3 \implies x + 1 = 0 \implies x = -1 \] So the x-intercept is at \( (-1, 0) \).
Graph: The graph of this function will show a cubic curve that passes through the point \( (-1, 0) \) and has its local maximum and minimum determined by the derivative.
If there's something specific you need help with regarding this function, feel free to ask!
