Find the extreme values of the function and where they occur. -y = x² + 2x - 3 A) Absolute minimum is 1 at x = 4. B) Absolute minimum is -4 at x = -1. C) Absolute minimum is -1 at x = 4. D) Absolute minimum is 1 at x = -4.

Question

Quizplus · Accepted Answer

The function given is $y = x^2 + 2x - 3$. To find the extreme values, we first find the derivative of the function, which is $y' = 2x + 2$. Setting the derivative equal to zero gives us the critical points: $2x + 2 = 0 \Rightarrow x = -1$. To determine if this critical point is a minimum or maximum, we can use the second derivative test or simply observe that the coefficient of $x^2$ is positive, indicating a parabola that opens upwards, thus the critical point at $x = -1$ is a minimum. Substituting $x = -1$ into the original function gives $y = (-1)^2 + 2(-1) - 3 = 1 - 2 - 3 = -4$, indicating an absolute minimum of -4 occurs at $x = -1$.

Find the Extreme Values of the Function and Where They