APPLICATION OF DERIVATIVES

 $If\ f^{\ '}\left(x\right)\ \ge0\ \ \ \ ,\ \forall\ x\in R\ then\ f\ is\$  

• strictly increasing on R

• strictly decreasing on R

• increasing on R

• decreasing on R

 $The\ function\ f\left(x\right)=e^x\ is$  

• strictly increasing on R

• strictly decreasing on R

• increasing on R

•  decreasing on R

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

•  $\left(-\infty,\ \infty\right)$  

•  $\left(2,\ 6\right)$  

•  $\left(-\infty,\ 4\right)$ 

•  $\left(4,\ \infty\right)$  

 $The\ slope\ of\ the\ \tan gent\ to\ the\ curve\ y=\ x^2+2\ at\ the\ point\ \left(2,\ 6\right)$  

• 4

• 6

• -6

• -4

 $The\ \min.\ value\ of\ f\left(x\right)=x^2-6x+5\ is$  

• 4

• -6

• 6

• -4

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

•  $60^0$  

•  $30^0$  

•  $90^0$  

•  $45^0$  

 $The\ equation\ \ of\ the\ \ \tan gent\ \ \ to\ the\ curve\ y^2=4ax\ at\ the\ point\ (at^2,\ 2at)\ is$  

•  $ty=x+at^2$  

•  $tx+y=at^3$  

•  $ty=x–at^2$  

• none of these

The maximum and minimum value of 3 sin x + 4 cos x +10 is

• 17 and 3

• 15 and 5

• 12 and 10

• None of these

Let f (x) = x³ – 6x² + 9x + 18, then f (x) is strictly decreasing in

• (–∞, 1]

• [3, ∞)

• (–∞, 1] U [3, ∞)

• [1, 3]

The absolute minimum value of x⁴ – x² – 2x+ 5

• is equal to 5

• is equal to 3

• is equal to 7

• does not exist