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1.7 Integration

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Question 57

The curve $C\,$ has equation $y = f (x)$ , $x > 0$ .

Given that

$C\,$ passes through the point $P (4, 5)$
$f′(x)=12x2+x−3\displaystyle f'(x) = \frac{12}{x^2} + \sqrt{x} - 3$

Find the equation of the tangent to $C\,$ at $P$ . Write your answer in the form $y = m x + c$ , where $m\,$ and $c\,$ are constants to be found.

[4]

Find, in simplest form, $f (x)$ .

[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

Question bank

1.7 Integration

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Question 57

The curve $C\,$ has equation $y = f (x)$ , $x > 0$ .

Given that

$C\,$ passes through the point $P (4, 5)$
$f′(x)=12x2+x−3\displaystyle f'(x) = \frac{12}{x^2} + \sqrt{x} - 3$

Find the equation of the tangent to $C\,$ at $P$ . Write your answer in the form $y = m x + c$ , where $m\,$ and $c\,$ are constants to be found.

[4]

Find, in simplest form, $f (x)$ .

[5]

Markscheme

1.7 Integration Questions

A Level
Maths
1.7 Integration