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The graph of \(f(x)\) is drawn below. Draw a sketch of \(f^{\prime}(x)\) on the same graph. (2 marks)
\(\text{Plot x-intercepts at the x-values of turning points.}\)
\(\text{Determine if gradient of}\ f(x)\ \text{is positive/negative to draw shape.}\)
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`.
On the diagram above, sketch the graph of the derivative `f^{′}(x)`. (3 marks)
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The diagram shows the graph of a function `y = f(x)`.
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i. `f^{′}(x) < 0\ text(when)`
`-1 < x < 3`
ii. `text(As)\ x -> oo,`
`f^{′}(x) -> 0`
iii.
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^{′}(x)` , clearly indicating its features at `x = 1` and at `x = 3`, and the shape of the graph as `x -> oo`. (3 marks)
