Home Quiz A Ultimate quiz on "Derivative"!!
Preview (10 questions)
1 Question
πριν 30 δευτερόλεπτα
Q.

What is the definition of the derivative of a function at a point?

The integral of the function at that point

The value of the function at that point

The area under the curve

The slope of the tangent line to the graph of the function at that point
2 Question
πριν 30 δευτερόλεπτα
Q.

Which of the following is the basic formula for the derivative of a function f(x)?

f ( x + h ) − f ( x ) ( x + h ) − x = f ( x + h ) − f ( x ) h

f(x) is, f'(x) = lim ₕ → ₀ [ f(x + h)

y = f(x)

lim h→0 [f(x + h) - f(x)] / h
3 Question
πριν 30 δευτερόλεπτα
Q.

If a function f(x) is not differentiable at a point, what can be true?

The function may have a corner or cusp at that point

The function may have a vertical asymptote at that point

The function may not be continuous at that point

All of the above
4 Question
πριν 30 δευτερόλεπτα
Q.

What is the derivative of a constant function f(x)=c, where c is a constant?

0

1

Undefined

C
5 Question
πριν 30 δευτερόλεπτα
Q.

If the derivative of a function 𝑓(x) is positive at a point, what does this indicate about the function f(x)?

The function has a local minimum at that point

The function has a local maximum at that point

The function is increasing at that point

The function is decreasing at that point
6 Question
πριν 30 δευτερόλεπτα
Q.

Which of the following is true for a function that has a local maximum at x=a?

f′(a)≠0

𝑓′(𝑎)≠0

f′(a)=01

𝑓′(𝑎)=0
7 Question
πριν 30 δευτερόλεπτα
Q.

If f(x) is differentiable at a point and f (x)=0, what does it imply?

The function is increasing at that point

The function is not defined at that point

The function is not continuous at that point

There is a horizontal tangent at that point
8 Question
πριν 30 δευτερόλεπτα
Q.

Which of the following is true about the second derivative of a function at a point where 𝑓′′(𝑥)>0f′′(x)>0?

The function is concave up at that point

The function has a local minimum at that point

The function has a local maximum at that point

The function is concave down at that point
9 Question
πριν 30 δευτερόλεπτα
Q.

Which of the following is an example of a function that is continuous but not differentiable at a point?

f(y) = |y|

f(x) = |y|

f(x) = |x|

f(x) - |x| at x = 0
10 Question
πριν 30 δευτερόλεπτα
Q.

Which rule is used to differentiate the product of two functions?

Sum Rule

Product Rule

Chain Rule

Quotient Rule