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DiffAbl1: Ableitung und Differenzierbarkeit (e) Flashcards | StudBud

Explore/DiffAbl1: Ableitung und Differenzierbarkeit (e)

DiffAbl1: Ableitung und Differenzierbarkeit (e)

8 terms·StudBud Administration·35 plays

#derivative #differentiation #continous #continuity #differential quotient #limit

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Questions 8

Answers

1
Is the function continous and/or differentiable at x = –7?
continous and differentiable at x = -7
neither continuous nor differentiable at x = -7
differentiable, but not continous at x = -7
continous, but not differentiable at x = -7
2
Find the derivative of f (x ) = 2x.
x2
0
2
not defined
3
Estimate the value of the derivative of the function f at x = 2. ⇒ f '(2)≈ ?
0.8
– 0.1
0.1
not defined
4
f ' (2)= –1 means
The gradient of f at x = 2 equals –1.
The tangent to the curve of f goes through the point (2 , –1).
The gradient of f at x = –1 equals 2.
The function value of f at x = 2 equals –1.
5
Is the function f(x)= 2– ³√(x) continuous and/or differentiable at x = 0 ?
continous and differentiable at x = 0
differentiable, but not continous at x = 0
continous, but not differentiable at x = 0
neither continuous nor differentiable at x = 0
6
Which answer is WRONG? The derivative f ' (x) of a function f is
the gradient of the graph of the function f
the limit of ( f(x+h) – f(x) ) / h for h → 0
the rate of change of the function f
the tangent to the graph of f
7
Is the function differentiable at x = 0 ?
No, because the value of the derivative is ∞ at x = 0.
No, because the function is not even continous at x = 0.
Yes, the function is differentiable at x = 0.
No, because at x = 0 the gradient on the left and right are not equal.
8
Find the derivative of the function f (x ) = 5.
0
not defined
5
5x