smc-2830-10-Find f(x) given f'(x)

Calculus, MET2 2020 VCAA 6 MC

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

The corresponding part of the graph of `y=f(x)` is best represented by

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`B`

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`text(By elimination:)`

`text(Two stationary points exist where)\ \ f^{‘}(x) =0\ \ text(and)\ \ x<0.`

`=>\ text(Eliminate)\ \ E, C, D`

`text{No other stationary points exist}\ →\ f^{‘}(x) !=0\ \ text(for)\ \ x>0.`

`=>\ text(Eliminate)\ \ E`

`=> B`

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

Which of the following could represent the graph of the function `f (x)?`

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`D`

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`text(A gradient table of the graph:)`

`=> D`

If `f prime (x) = 3x^2 - 4`, which one of the following graphs could represent the graph of `y = f (x)`?

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`B`

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`f prime (x) = 3x^2 – 4`

`:. f(x)\ text(is a cubic with two stationary points.)`

`=> B`