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2. APPLICATION OF DERIVATIVES

Authored by NOUSHEEN SHAFY

Mathematics, Fun

12th Grade

CCSS covered

Used 10+ times

2. APPLICATION OF DERIVATIVES
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10 questions

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1.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

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

2.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

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

f"(x) = 2 + ex + cosx
f"(x) = 2x + ex + cosx
f"(x) = 2x + xex - cosx
f"(x) = 2x + ex + sinx

Tags

CCSS.HSF.IF.A.2

3.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

 If f ′(x) ≥0    , ∀ x∈R then f is 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

4.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

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

strictly increasing on R

strictly decreasing on R

increasing on R

 decreasing on R

5.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

 The slope of the tan⁡gent to the curve y= x2+2 at the point (2, 6)The\ slope\ of\ the\ \tan gent\ to\ the\ curve\ y=\ x^2+2\ at\ the\ point\ \left(2,\ 6\right)  

4

6

-6

-4

6.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

 The min⁡. value of f(x)=x2−6x+5 isThe\ \min.\ value\ of\ f\left(x\right)=x^2-6x+5\ is  

4

-6

6

-4

7.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

 The equation  of the  tan⁡gent   to the curve y2=4ax at the point (at2, 2at) isThe\ equation\ \ of\ the\ \ \tan gent\ \ \ to\ the\ curve\ y^2=4ax\ at\ the\ point\ (at^2,\ 2at)\ is  

 ty=x+at2ty=x+at^2  

 tx+y=at3tx+y=at^3  

 ty=x–at2ty=x–at^2  

none of these

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