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Differentiation

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Question 517

The thermal profile of a synthetic crystal is modeled by the equation

5t−3tT+T2=23,T≥0 5^t - 3tT + T^2 = 23, \quad T \ge 0 5t−3tT+T2=23,T≥0

where TTT is the temperature in degrees Celsius and ttt is the time in hours. A specific observation point PPP on the profile has t=1t = 1t=1.

a.

Find the temperature TTT at point PPP.

[2]
b.

Find an expression for dTdt\frac{dT}{dt}dtdT​ in terms of TTT and ttt.

[3]
c.

The tangent to the profile at point PPP intersects the horizontal ttt-axis at point QQQ.

Determine the ttt-coordinate of QQQ, giving your answer in the form aln⁡5+bcln⁡5+d\frac{a \ln 5 + b}{c \ln 5 + d}cln5+daln5+b​ where a,b,c,a, b, c,a,b,c, and ddd are integers to be found.

[4]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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