11.1 Integrating Standard Functions

List view

The cross-section of a precision-engineered lens is modeled by a curve $y = f (x)$ , for $x > 0$ . The rate of change of the gradient of the profile is given by

$\frac{15}{4\sqrt{x^7}} - 6x$

A point $P (1, 1.5)$ lies on the boundary of the lens profile.

Given that the gradient of the curve $f^{'} (x) = 0.75$ at point $P$ ,

find the equation of the normal at $P$ , writing your answer in the form $y = m x + c$ , where $m$ and $c$ are constants,

[3]

find $f (x)$ .

[5]

11.1 Integrating Standard Functions Questions

Practise Edexcel A Level Maths 11.1 Integrating Standard Functions with exam-style questions for A Level Maths. 81 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.