2. APPLICATION OF DERIVATIVES

If the position of a particle is represented by x(t) = -t² + 1, what is its instantaneous velocity at t = 1?  

• v = 0
• v = 1
• v = -1
• v = -2

Tags

CCSS.HSN.VM.A.3

Find the second derivative of
f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx
• f"(x) = 2x + e^x + cosx
• f"(x) = 2x + xe^x - cosx
• f"(x) = 2x + e^x + sinx

Tags

CCSS.HSF.IF.A.2

 $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

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

• 4

• 6

• -6

• -4

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

• 4

• -6

• 6

• -4

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

•  $ty=x+at^2$  

•  $tx+y=at^3$  

•  $ty=x–at^2$  

• 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

Tags

CCSS.HSF.TF.A.4

Use differential to approximate  $\sqrt{36.6}$  

• 6.01

• 6.05

• 6.1

• 6.09

The absolute minimum value of   $x^4-x^2-2x+5$  

• 5
  

• 3

• 7

• does not exist