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9.9 Using Second Derivatives

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Question 16

The temperature, $T$ degrees Celsius, of a cooling laser component $t$ minutes after activation is modeled by the function $T = f (t)$ for $t > 0$ .

It is given that:

the point $P (4, 10)$ lies on the curve $T = f (t)$
the rate of change of temperature is $12\sqrt{t} + \frac{k}{t^2}$ , where $k$ is a constant
the rate of change of temperature, $f^{'} (t)$ , has a stationary point at $P$

Find the exact value of $k$ .

[3]

Determine an expression for $f (t)$ , giving your answer in its simplest form.

[5]

Markscheme

9.9 Using Second Derivatives Questions

A Level
Maths
9.9 Using Second Derivatives

57 exam-style questions on Edexcel A Level Maths 9.9 Using Second Derivatives. Each one has a worked solution and a mark scheme showing where the marks go.

9.9 Using Second Derivatives

Question bank

9.9 Using Second Derivatives

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Question 16

The temperature, $T$ degrees Celsius, of a cooling laser component $t$ minutes after activation is modeled by the function $T = f (t)$ for $t > 0$ .

It is given that:

the point $P (4, 10)$ lies on the curve $T = f (t)$
the rate of change of temperature is $12\sqrt{t} + \frac{k}{t^2}$ , where $k$ is a constant
the rate of change of temperature, $f^{'} (t)$ , has a stationary point at $P$

Find the exact value of $k$ .

[3]

Determine an expression for $f (t)$ , giving your answer in its simplest form.

[5]

Markscheme

9.9 Using Second Derivatives Questions

A Level
Maths
9.9 Using Second Derivatives

57 exam-style questions on Edexcel A Level Maths 9.9 Using Second Derivatives. Each one has a worked solution and a mark scheme showing where the marks go.