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DiffAbl1-2a: Ableitung und erste Regeln (e) Flashcards | StudBud

Explore/DiffAbl1-2a: Ableitung und erste Regeln (e)

DiffAbl1-2a: Ableitung und erste Regeln (e)

9 terms·StudBud Administration·13 plays

# Ableitungsbegriff # Definition der Ableitung als Steigungsfunktion # Erste Ableitungsregeln # Derivative # Rules of Differentiation

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Questions 9

Answers

1
Estimate the value of the derivative of the function f at x = 1. ⇒ f '(1)≈ ?
f '(1) is not defined
f '(1) ≈ 0.8
f '(1) ≈ – 0.1
f '(1) ≈ 0.1
2
Find the derivative of the function f (x ) = x ³ – x +5.
f ' (x) = 3x 2 – x +5
f ' (x) = 3x 2 – 1
f ' (x) = 2x 2 – 1
f ' (x) = 3x 2 – x
3
Which answer is WRONG? The derivative f ' (x) of a function f gives
Empty choice
the tangent line to the graph of f
the rate of change of the function f
the gradient of the graph of the function f
4
Determine f ' (x), if f (x) = 3 – x / 2 .
f ' (x) = 2 . 5
f ' (x) = – 0.5
f ' (x) = 3
none of the other results
5
Determine f ' (x), if f (x) = 3 sin (x) + e^x
f ' (x) = – 3 cos (x ) + ex
f ' (x) = 3 cos (x ) + ex
f ' (x) = cos (x ) + ex
none of the other results
6
Is f differentiable at x = –1 ?
No, because the function f is not even continous at x = –1.
Yes, the function f is differentiable at x = –1.
No, because the value of the derivative is ∞ at x = –1.
No, because at x = –1 the slope of f on the left and right are not equal.
7
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.
8
Find the derivative of the function f (x ) = 5.
not defined
f '(x) = 0
f '(x) = 5x
f '(x) = 5
9
Determine the gradient of the curve of y = x ² at x = 4
none of the others
8
4
16