1.8.2 Integrating x^n

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Question 67

The curve C has equation $\text{f}(x)$ where $x > 0$ .

Given that

$f′(x)=(x+2)2xx\text{f}'(x) = \dfrac{(x + 2)^2}{x\sqrt{x}}$
the point $P (9, 30)$ lies on C

a.

(i) Find the value of the gradient of the curve at $P$ .

(ii) Hence find the equation of the tangent to $C$ at $P$ , giving your answer in the form $a x + b y + c = 0$ , where $a$ , $b$ and $c$ are integers to be found.

[4]

b.

Find $f(x)\text{f}(x)$ , simplifying your answer.

[6]

1.8.2 Integrating x^n

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Question 67

The curve C has equation $\text{f}(x)$ where $x > 0$ .

Given that

$f′(x)=(x+2)2xx\text{f}'(x) = \dfrac{(x + 2)^2}{x\sqrt{x}}$
the point $P (9, 30)$ lies on C

a.

(i) Find the value of the gradient of the curve at $P$ .

(ii) Hence find the equation of the tangent to $C$ at $P$ , giving your answer in the form $a x + b y + c = 0$ , where $a$ , $b$ and $c$ are integers to be found.

[4]

b.

Find $f(x)\text{f}(x)$ , simplifying your answer.

[6]

1.8.2 Integrating x^n

Question 67

1.8.2 Integrating x^n Questions

1.8.2 Integrating x^n

Question 67

1.8.2 Integrating x^n Questions