Applications of Derivatives

Applications of Derivatives

Assessment

Assessment

Created by

Keren Zaks

Mathematics, Other

11th - 12th Grade

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20 questions

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1.

Multiple Choice

15 mins

1 pt

Let f be the function given by f(x) = x3.  What are all values of c that satisfy the conclusion of the Mean Value Theorem on the closed interval [-1, 2]?  (No calculator)

0 only

1 only

√3 only

-1 and 1

2.

Multiple Choice

15 mins

1 pt

If   x=0.5x=0.5  is a critical point of  f(x)f\left(x\right)  and  f(x) = cos2xlnxf''\left(x\right)\ =\ \cos^2x\cdot\ln x  then  x=0.5x=0.5  is a 

local maximum

local minimum

neither

3.

Multiple Choice

15 mins

1 pt

 Which of the following is NOT a critical point of f(x) = exx2f\left(x\right)\ =\ e^x\cdot x^2 ?

 x=0x=0  

 x=1x=1  

 x=2x=-2  

4.

Multiple Choice

15 mins

1 pt

Where is the point of inflection for the function  f(x) = x3 +6x2f\left(x\right)\ =\ x^{3\ }+6x^2  ?

 x=0x=0  

 x=4x=-4  

 x=2x=-2  

 x=4x=4  

5.

Multiple Choice

15 mins

1 pt

On what interval(s) is the function
 f(x) = x3 +6x2f\left(x\right)\ =\ x^{3\ }+6x^2  
concave up?

 (,)\left(-\infty,\infty\right)  

 (,2)\left(-\infty,-2\right)  

 (2,)\left(-2,\infty\right)  

 (0,)\left(0,\infty\right)  

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