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≥0where 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.
Find the temperature TTT at point PPP.
Find an expression for dTdt\frac{dT}{dt}dtdT in terms of TTT and ttt.
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 aln5+bcln5+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.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
