# Applications Of Derivatives Assessment Test

10 Questions | Total Attempts: 129  Settings  Applications of derivatives are using derivatives to determine information about limits, estimation of solutions to equations, graphs of functions and optimization problems. Take our assessment test to assess your knowledge of applications of derivatives.

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• 1.
The minimum value of ax + by, where xy = r , is (r, ab >0)...
• A.

2r √ab

• B.

2ab√r

• C.

–2r √ab

• D.

None of the above

• 2.
The function 2tan x – 3tan x + 12tanx + 3, x Î is...
• A.

Decreasing

• B.

Increasing

• C.

None of the above

• D.

I don't know

• 3.
The absolute minimum value of x4-x2-2x+5...
• A.

Is equal to 5

• B.

Is equal to 3

• C.

Is equal to 7

• D.

Does not exist

• 4.
If a, b, c, d are four positive real numbers such that abcd =1, then minimum value of (1+ a) (1 + b) (1 + c) (1 + d) is...
• A.

16

• B.

13

• C.

17

• D.

18

• 5.
Rolle’s theorem holds for the function x3 + bx2 + cx, 1 < x < 2 at the point 4/3, the value of b and c are...
• A.

B = 8, c = - 5

• B.

B = -5, c = 8

• C.

B = 5, c = -8

• D.

B = -5, c = -8

• 6.
The number of value of k for which the equation x3 – 3x + k = 0 has two different roots lying in the interval (0, 1) are...
• A.

Infinitely many

• B.

2

• C.

3

• D.

0

• 7.
Let f (x) = (4–x2)2/3 , then f has a...
• A.

A local maxima at x = 0

• B.

A local maxima at x = 2

• C.

A local maxima at x = –1

• D.

None of the above

• 8.
L'Hopital's rule states that the limit of a function of the form f(x) / g(x) is equal to the limit of the derivative off(x) / g(x).
• A.

Always true

• B.

Often true

• C.

Occasionally true

• D.

Never true

• 9.
Newton's method is used to approximate the extrema of a function.
• A.

Always true

• B.

Often true

• C.

Occasionally true

• D.

Never true

• 10.
An absolute maximum or minimum must occur at a critical point or at an endpoint.
• A.

True

• B.

False

• C.

Maybe

• D.

Depends on some factors