The concentration of a specific chemical dye in a test vat, CCC (measured in mg/L), is modeled by the function
C(t)=2t−11t+10,t>0 C(t) = 2t - 11\sqrt{t} + 10, \quad t > 0 C(t)=2t−11t+10,t>0where t t\,t is the time in hours since the dye was introduced.
Determine the two values of t t\,t for which the concentration is exactly 5 mg/L.
Find the value of t t\,t for which C′′(t)=1132\displaystyle C''(t) = \frac{11}{32}C′′(t)=3211.
425 exam-style questions on OCR A Level Maths 1.7 Differentiation, covering 1.7.1 Derivative as gradient of the tangent, 1.7.2 Gradient of the tangent at a point, 1.7.3 Sketching the gradient function, 1.7.4 Second derivatives, 1.7.5 Second derivative as rate of change of gradient, 1.7.6 Convex, concave and points of inflection (A-level only), 1.7.7 Differentiation from first principles for powers of x, 1.7.8 Differentiation from first principles for sin x and cos x (A-level only), 1.7.9 Differentiating x^n, 1.7.10 Differentiating e^(kx) and a^(kx) (A-level only), 1.7.11 Differentiating trigonometric functions (A-level only), 1.7.12 Derivative of ln x (A-level only), 1.7.13 Tangents and normals, 1.7.14 Stationary points, 1.7.15 Increasing and decreasing functions, 1.7.16 Points of inflection (A-level only), 1.7.17 Product and quotient rules (A-level only), 1.7.18 Chain rule (A-level only), 1.7.19 Parametric and implicit differentiation (A-level only), 1.7.20 Constructing differential equations (A-level only), and 1.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.