Question

Let ${\text{S}}_1$is set of minima and ${\text{S}}_2$is set of maxima for the curve ${\text{y=9x}}^4+12x^3-36x^2-25$ then

• A. ${\text{S}}_1=\{-2,-1\}{\text{S}}_2=\left\{0\right\}$
• B. ${\text{S}}_1=\{-2,1\}{\text{S}}_2=\left\{0\right\}$
• C. ${\text{S}}_1=\{-2,1\}{\text{S}}_2=\{-1\}$
• D. ${\text{S}}_1=\{-2,2\}{\text{S}}_2=\left\{0\right\}$

Answer 1

The correct option is B

${\text{S}}_1=\{-2,1\}{\text{S}}_2=\left\{0\right\}$

Explanation for the correct option:

Finding the set of maxima and the set of minima

Given the curve is ${\text{y=9x}}^4+12x^3-36x^2-25$

Differentiating on both sides ,we get

$$\begin{gathered} \frac{dy}{dx}=36x^3+36x^2-72x \\ \frac{dy}{dx}=36x(x^2+x-2) \\ \frac{dy}{dx}=36x(x^2+2x-x-2) \\ \frac{dy}{dx}=36x(x+2)(x-1) \end{gathered}$$

Critical points are $\{0,-2,1\}$

${\text{S}}_1=\{-2,1\}{\text{S}}_2=\left\{0\right\}$

Hence ,the correct option is (B)