The concentration CCC (in mg/L) of a chemical catalyst over time ttt (in minutes) is modeled by the function
C(t)=(2t−3)4e−2t,t≥1.5 C(t) = (2t - 3)^4 e^{-2t}, \quad t \ge 1.5 C(t)=(2t−3)4e−2t,t≥1.5Show that
C′(t)=A(2t−3)3(7−2t)e−2t C'(t) = A(2t - 3)^3 (7 - 2t) e^{-2t} C′(t)=A(2t−3)3(7−2t)e−2twhere A A\,A is a constant to be found.
Hence find the exact coordinates of the two stationary points on the curve with equation y=C(t)y = C(t)y=C(t).
A secondary reaction is modeled by the function HHH, defined by
H(t)=5C(t+0.5) H(t) = 5 C(t + 0.5) H(t)=5C(t+0.5)Find the coordinates of the maximum stationary point on the curve with equation y=H(t)y = H(t)y=H(t).
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.