Application of Calculus(Stationary Points)

Which of the following options represent the coordinates of the stationary point(s) of 

 $y=x^3-3x^2-9x+4$  

•  $\left(-1,3\right)\ \&\ \left(-12,12\right)$  

•  $\left(-1,9\right)\ \text{}\&\ \left(3,-23\right)$  

•  $\left(-1,-12\right)\ \&\ \left(3,12\right)$  

•  $\left(-1,3\right)\ \&\ \left(9,-23\right)$  

The critical points of the function

 $y=3x^4-8x^3-30x^2+72x$  are given by  $\left(-2,-152\right)$  , $\left(1,37\right)$  and  $\left(3,-27\right)$  .Which of the following statements are true.

• Maximum values occur at  $\left(1,37\right)\ \&\ \left(3,-27\right)$  

• Minimum values occur at  $\left(-2,-152\right)\ \&\ \left(3,-27\right)$  

• Minimum values occur at  $\left(-2,-152\right)\ \&\ \left(1,37\right)$  

• Maximum value only occurs at  $\left(3,-27\right)$  

Which of the following options represent the stationary point(s) of $y=4x+\frac{1}{x}$  ?

•  $\left(\frac{1}{2},-\frac{1}{2}\right)$  

•  $\left(4,-4\right)\ \&\ \left(\frac{1}{2},-\frac{1}{2}\right)$  

•  $\left(\frac{1}{2}.4\right)\ \&\ \left(-\frac{1}{2},-4\right)$  

•  $\left(4,-4\right)$  

The stationary points of a curve are given by $\left(5,11\frac{2}{3}\right)\ \&\ \left(3,15\right)$ . The expression which best describes  $\frac{dy}{dx}$  is given by: 

•  $\frac{dy}{dx\ }=x^2+18x+45$  

•  $\frac{dy}{dx\ }=x^2+8x+15$  

•  $\frac{dy}{dx\ }=3x^2-80x+525$  

•  $\frac{dy}{dx\ }=x^2-8x+15$  

A farmer wants to create a temporary pen for his sheep. He has 100 meters of fencing and a stone wall available. He decides that the shape of his pen would be a rectangle. Which of the following equations represent the area of the enclosure?

Hint: Please copy or take note of this question as the answer can help for question (6).

• $A=50x-x^2$

• $A=100x^2$

• $A=100x-2x^2$

• $A=200x$

A farmer wants to create a temporary pen for his sheep. He has 100 meters of fencing and a stone wall available. He decides that the shape of his pen would be a rectangle. What is the maximum area that the farmer could enclose?

• $1\ 250\ m^2$

• $2\ 500\ m^2$

• $1\ 875\ m^2$

• $625\ m^2$