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1.7 Integration

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Question 92

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]

Markscheme

1.7 Integration Questions

A Level
Maths
1.7 Integration

133 exam-style questions on CCEA A Level Maths 1.7 Integration, covering 1.7.1 Integration, 1.7.2 Integration, and 1.7.3 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

1.7 Integration

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1.7 Integration

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Question 92

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]

Markscheme

1.7 Integration Questions

A Level
Maths
1.7 Integration