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1.9.17 Concavity and the second derivative (A-level only)

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Question 30

The height of a biological culture, $H (t)$ millimetres, is observed over time $t\,$ hours for $t > 0$ .

Given that

$H′(t)=10t14+kt2−4\displaystyle H'(t) = 10t^{\frac{1}{4}} + \frac{k}{t^2} - 4$ , where $k\,$ is a constant
$H^{''} (t) = 0$ when $t = 16$

Determine the value of $k$ .

[3]

Given also that

$H (t) = 20$ when $t = 1$

Find an expression for $H (t)$ , giving each term in simplest form.

[4]

Markscheme

1.9.17 Concavity and the second derivative (A-level only) Questions

A Level
Maths
1.9.17 Concavity and the second derivative (A-level only)

57 exam-style questions on OCR (MEI) A Level Maths 1.9.17 Concavity and the second derivative (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

1.9.17 Concavity and the second derivative (A-level only)

Question bank

1.9.17 Concavity and the second derivative (A-level only)

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Question 30

The height of a biological culture, $H (t)$ millimetres, is observed over time $t\,$ hours for $t > 0$ .

Given that

$H′(t)=10t14+kt2−4\displaystyle H'(t) = 10t^{\frac{1}{4}} + \frac{k}{t^2} - 4$ , where $k\,$ is a constant
$H^{''} (t) = 0$ when $t = 16$

Determine the value of $k$ .

[3]

Given also that

$H (t) = 20$ when $t = 1$

Find an expression for $H (t)$ , giving each term in simplest form.

[4]

Markscheme

1.9.17 Concavity and the second derivative (A-level only) Questions

A Level
Maths
1.9.17 Concavity and the second derivative (A-level only)

57 exam-style questions on OCR (MEI) A Level Maths 1.9.17 Concavity and the second derivative (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.