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1.6 Differentiation

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Question 59

A landscape architect is designing a section of a path. The elevation $h\,$ of the path (in meters) relative to a reference level is modeled by the function

\frac{1}{12}x^4 + \sin x + 5

for $−π≤x≤π-\pi \le x \le \pi$ , where $x\,$ represents the horizontal distance in meters from a marker.

Determine whether the curve with equation $y = h (x)$ has a point of inflection at the point where $x = 0$ . Fully justify your answer.

[5]

Markscheme

1.6 Differentiation Questions

A Level
Maths
1.6 Differentiation

115 exam-style questions on CCEA A Level Maths 1.6 Differentiation, covering 1.6.1 Differentiation, 1.6.2 Differentiation, 1.6.3 Differentiation, 1.6.4 Differentiation, 1.6.5 Differentiation, 1.6.6 Differentiation, and 1.6.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

1.6 Differentiation

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1.6 Differentiation

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Question 59

A landscape architect is designing a section of a path. The elevation $h\,$ of the path (in meters) relative to a reference level is modeled by the function

\frac{1}{12}x^4 + \sin x + 5

for $−π≤x≤π-\pi \le x \le \pi$ , where $x\,$ represents the horizontal distance in meters from a marker.

Determine whether the curve with equation $y = h (x)$ has a point of inflection at the point where $x = 0$ . Fully justify your answer.

[5]

Markscheme

1.6 Differentiation Questions

A Level
Maths
1.6 Differentiation