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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
