The curve C has equation $\mathrm{f}(x), x > 0$ . Given that:

the point $P (9, - 2)$ lies on $C$
$f′(x)=3x2+ax+b2x\mathrm{f}'(x) = \dfrac{3x^2 + ax + b}{2\sqrt{x}}$ , where $a$ and $b$ are constants
the gradient of the tangent to $C$ at $P$ is $35$

Show that $9 a + b = - 33$ .

Given also that $a - b = 13$

Find, in simplest form, $f(x)\mathrm{f}(x)$ .

Curve $C$ is transformed to the curve with equation $\mathrm{f}(x + 4)$ . Given that point $P$ is transformed to the point $Q$ ,

State the coordinates of $Q$ .

The curve C has equation $\mathrm{f}(x), x > 0$ . Given that:

the point $P (9, - 2)$ lies on $C$
$f′(x)=3x2+ax+b2x\mathrm{f}'(x) = \dfrac{3x^2 + ax + b}{2\sqrt{x}}$ , where $a$ and $b$ are constants
the gradient of the tangent to $C$ at $P$ is $35$

Show that $9 a + b = - 33$ .

Given also that $a - b = 13$

Find, in simplest form, $f(x)\mathrm{f}(x)$ .

Curve $C$ is transformed to the curve with equation $\mathrm{f}(x + 4)$ . Given that point $P$ is transformed to the point $Q$ ,

State the coordinates of $Q$ .

1.11.2 Integrating standard functions

1.11.2 Integrating standard functions Questions