The yield, YYY, of a certain chemical reaction is related to the operating temperature, xxx, by the equation
Y=5x+15(2x−8)2,x∈R,x≠4 Y = \frac{5x + 15}{(2x - 8)^2}, \quad x \in \mathbb{R}, \quad x \neq 4 Y=(2x−8)25x+15,x∈R,x=4where x x\,x is measured in degrees Celsius.
Use calculus to find the set of values of x x\,x for which the yield Y Y\,Y is increasing.
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, 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). Each one has a worked solution and a mark scheme showing where the marks go.