smc-2830-20-Find f'(x) graph given f(x)

Calculus, MET2 2022 VCAA 7 MC

The graph of `y=f(x)` is shown below.

The graph of `y=f^{\prime}(x)`, the first derivative of `f(x)` with respect to `x` could be

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`E`

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`=>E`

Calculus, MET2 2021 VCAA 8 MC

The graph of the function `f` is shown below.

The graph corresponding to `f^{′}` is

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`E`

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`text(By elimination:)`

♦ Mean mark 40%.

`text{As} \ \ x to a^+ \ , \ f^{′}(x) to ∞`

`:. \ text{Eliminate}\ A, B, C`

`f(x) \ text{exists for} \ x ∈ (a,∞)`

`f^{′}(x) \ text{only exists for} \ \ x ∈ (a, ∞)`

`:. \ text{Eliminate}\ D`

`=> E`

Calculus, MET2 2019 VCAA 16 MC

Part of the graph of `y = f(x)` is shown below.

The corresponding part of the graph of `y = f^{\prime}(x)` is best represented by

A.		B.
C.		D.
E.

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`A`

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`text(By Elimination):`

`text(S.P. at)\ \ x = 5`

`=> f^{\prime}(x) = 0\ \ text(when)\ \ x = 0`

`text(Eliminate C, E)`

`text(Gradient is negative when)\ \ x < 5,\ \ text(and positive when)\ \ x >5`

`text(Eliminate B, D)`

`=> A`

Calculus, MET2 2008 VCAA 19 MC

The graph of a function `f` is shown below.

The graph of an antiderivative of `f` could be

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`B`

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`text(S)text(ince)\ \ f(x)>0\ \ text(for all)\ x,\ text(the)`

♦ Mean mark 50%.

`text(antiderivative function has no stationary)`

`text(points.)`

`=>\ text(Only B or E are possibilities.)`

`text(Also, the antiderivative function must have)`

`text(an increasing gradient for all)\ x.`

`=> B`

Calculus, MET2 2016 VCAA 3 MC

Part of the graph `y = f(x)` of the polynomial function `f` is shown below

`f prime (x) < 0` for

`x ∈ (−2, 0) uu (1/3, oo)`
`x ∈ (−9, 100/27)`
`x ∈ (−oo, −2) uu (1/3, oo)`
`x ∈ (−2, 1/3)`
`x ∈ (−oo, −2] uu (1, oo)`

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`C`

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`text(Outlining the sections of negative gradient:)`

`f prime (x) < 0`

`=> C`

Calculus, MET2 2011 VCAA 9 MC

The graph of the function `y = f(x)` is shown below.

Which if the following could be the graph of the derivative function `y = f′(x)`?

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`=> B`

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`text(Stationary points at)\ \ x = – 3, 0`

`:. f′(x)\ \ text(has)\ x text(-intercepts at)\ -3, 0.`

`text(Only)\ B, C or D\ text(possible).`

`text(By inspection of the)\ \ f(x)\ \ text(graph:)`

`f′(x) > 0quadtext(for)quadx < −3`

`text(Only)\ B\ text(satisfies.)`

`=> B`

Calculus, MET1 2007 VCAA 3

The diagram shows the graph of a function with domain `R`.

For the graph shown above, sketch on the same set of axes the graph of the derivative function. (3 marks)
Write down the domain of the derivative function. (1 mark)

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`R\ text(\)\ {0,3}`

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♦ Part (a) mean mark 42%, and part (b) mean mark 45%.

b. `text(Derivative does not exist at either sharp)`

`text(points or discontinuous points.)`

`:. R\ text(\)\ {0,3}`