A function f f\,f has domain R\mathbb{R}R and range {y∈R:y≥−4}\{y \in \mathbb{R} : y \ge -4\}{y∈R:y≥−4}. The gradient of the curve y=f(x)y = f(x)y=f(x) at any point (x,y)(x, y)(x,y) is given by dydx=(2x−8)ex\displaystyle \frac{dy}{dx} = (2x - 8)e^xdxdy=(2x−8)ex. Find an expression for f(x)f(x)f(x). Fully justify your answer.
Practise Edexcel A Level Maths 11.10 Solving Differential Equations with exam-style questions for A Level Maths. 35 questions, matched to the Edexcel A Level Maths (9MA0) 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.
