smc-1089-20-Graph f'(x) given f(x)

Calculus, 2ADV C3 EQ-Bank 1

The graph of \(f(x)\) is drawn below. Draw a sketch of \(f^{\prime}(x)\) on the same graph. (2 marks)

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\(\text{Plot x-intercepts at the x-values of turning points.}\)

\(\text{Determine if gradient of}\ f(x)\ \text{is positive/negative to draw shape.}\)

Calculus, 2ADV C3 2014 HSC 14e

The diagram shows the graph of a function `f(x)`.

The graph has a horizontal point of inflection at `A`, a point of inflection at `B` and a maximum turning point at `C`.

Sketch the graph of the derivative `f prime (x)`. (3 marks)

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Calculus, 2ADV C3 2009 HSC 8a

The diagram shows the graph of a function `y = f(x)`.

For which values of `x` is the derivative, `f^{′}(x)`, negative? (1 mark)

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What happens to `f^{′}(x)` for large values of `x`? (1 mark)

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Sketch the graph `y = f^{′}(x)`. (2 marks)

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`f^{′}(x) < 0\ text(when)`

`-1 < x < 3`
`text(As)\ x -> oo`

`f^{′}(x) -> 0`

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i. `f^{′}(x) < 0\ text(when)`

`-1 < x < 3`

♦♦ Exact data not available.

ii. `text(As)\ x -> oo,`

`f^{′}(x) -> 0`

♦♦ Exact data not available.
MARKER’S COMMENT: Poorly drawn graphs with axes not labelled and inaccurate scales were common.

iii.

Calculus, 2ADV C3 2011 HSC 9c

The graph `y = f(x)` in the diagram has a stationary point when `x = 1`, a point of inflection when `x = 3`, and a horizontal asymptote `y = –2`.

Sketch the graph `y = f prime (x)` , clearly indicating its features at `x = 1` and at `x = 3`, and the shape of the graph as `x -> oo`. (3 marks)

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♦ Mean mark 43%
IMPORTANT: Examiners regularly ask questions that require the graphing of an `f prime(x)` given the `f(x)` graph and vice-versa. KNOW IT!