Course home

9.9 Using Second Derivatives

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 7

The concentration of a specific catalyst in a bioreactor, $C\,$ mg/L, is monitored over a 12-hour production cycle. The concentration at time $t\,$ hours, for $\le t \le 12$ , is modeled by the function:

\frac{\sqrt{t}}{20}(24 + 10t - t^2) + 5

Given that $C\,$ has a stationary value at $\alpha$ :

Use calculus to show that $\alpha\,$ satisfies the equation

5\alpha^2 - 30\alpha - 24 = 0

[4]

Hence find the value of $α\alpha$ , giving your answer to 3 decimal places.

[2]

Use further calculus to prove that $C\,$ is a maximum at this value of $α\alpha$ .

[3]

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

Easy Medium Hard

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 7

\frac{\sqrt{t}}{20}(24 + 10t - t^2) + 5

Given that $C\,$ has a stationary value at $\alpha$ :

Use calculus to show that $\alpha\,$ satisfies the equation

5\alpha^2 - 30\alpha - 24 = 0

[4]

Hence find the value of $α\alpha$ , giving your answer to 3 decimal places.

[2]

Use further calculus to prove that $C\,$ is a maximum at this value of $α\alpha$ .

[3]

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.