2019 Nov P1 Q7

Question 7

$7.1$	Determine $f^\prime (x)$ from first principles if it is given that $f(x)=4-7x$ .	$(4)$
$7.2$	Determine $\frac{\displaystyle dy}{\displaystyle dx}$ if $y=4x^8+\sqrt{x^3}$	$(3)$
$7.3$	Given: $y=ax^2+a$ Determine:
$\quad 7.3.1$	$\frac{\displaystyle dy}{\displaystyle dx}$	$(1)$
$\quad 7.3.2$	$\frac{\displaystyle dy}{\displaystyle da}$	$(2)$
$7.4$	The curve with the equation $y=x+\frac{\displaystyle 12}{\displaystyle x}$ passes through the point $A(2\; ;\, b)$ . Determine the equation of the line perpendicular to the tangent to the curve at $A$ .	$(4)$
		$\textbf{[14]}$