Application of Derivatives

A fn is said to be increasing fn if f'(x) is

• $\ge0$

• $\le0$

• $=0$

• $\ne0$

A fn is said to be increasing fn if f'(x) is

• $\ge0$

• $\le0$

• $=0$

• $\ne0$

Find the interval(s) where f(x)=6x²-x³ is increasing.

• (-4,0)
• (0,4)
• (-∞, 0)∪(4, ∞)
• (-∞, -4 )∪(0, ∞)

How many extrema are in the picture?

• 2
• 3
• 4
• 5

The equation of normal to the curve  $3x^2-y^2=8$  which is parallel to the line  $x+3y=8$  is

•  $3x-y=8$  

•  $3x+y+8=0$  

•  $x+3y\ ±\ 8=0$  

•  $x+3y=0$  

 $The\ function\ f\left(x\right)=\ x^2-8x+12\ is\ strictly\ decrea\sin g\ in$  

•  $\left(-\infty,\ \infty\right)$  

•  $\left(2,\ 6\right)$  

•  $\left(-\infty,\ 4\right)$ 

•  $\left(4,\ \infty\right)$  

The interval in which $y=x^2e^{–x}$  is increasing is

•  $\left(-2,\ 0\right)$  

•  $\left(-\infty,\ \infty\right)$  

•  $\left(2,\ \infty\right)$  

•  $\left(0,\ 2\right)$  

Over what interval(s) is f(x) decreasing?

• (-3, 1)
• (-∞, -5) ∪ (0, 2)
• (-∞, -3) ∪ (1, ∞)
• (-5, 0) ∪ (2, ∞)

 $The\ angle\ between\ the\ lines\ y\ =\ \sqrt{3}x\ +100\ and\ \ \sqrt{3}y\ =x\ +200\ is$  

•  $60^0$  

•  $30^0$  

•  $90^0$  

•  $45^0$  

What are the two numbers that will give the maximum product?

• 40 and 40

• 20 and 60

• 45 and 35

• 30 and 50