The critical point for the function y = 3x² + 5x + 2 is at A)x = -5/6. B)x = 3/5. C)x = -3/2. D)There is no critical point.

Question

Quizplus · Accepted Answer

To find the critical point of the function $y = 3x^{12} + 5x + 2$, we need to take the derivative and set it equal to zero. The derivative is $y' = 36x^{11} + 5$. Setting this equal to zero gives $36x^{11} + 5 = 0$, which simplifies to $x^{11} = -\frac{5}{36}$. The real root of this equation is $x = -\left(\frac{5}{36}\right)^{\frac{1}{11}}$, which is approximately $x = -\frac{5}{6}$, making option A the correct choice.

The Critical Point for the Function Y = 3x2

The Critical Point for the Function Y = 3x²