A specialized hydraulic piston's displacement DDD (in mm) relative to a benchmark is modeled by the equation:
D(t)=25∣5t+8∣−6,t∈R D(t) = \frac{2}{5}|5t + 8| - 6, \quad t \in \mathbb{R} D(t)=52∣5t+8∣−6,t∈Rwhere t t\,t is the time in seconds.
State the coordinates of the vertex, VVV, of the graph of y=D(t)y = D(t)y=D(t).
Using algebra, determine the set of values of t t\,t for which
D(t)>2−15t D(t) > 2 - \frac{1}{5}t D(t)>2−51tSketch the graph with equation y=∣D(t)∣y = |D(t)|y=∣D(t)∣, stating the coordinates of the local maximum point and each local minimum point.
181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.