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 $A$ .	$(4)$
		$\textbf{[14]}$

$7.1$	Determine $f^\prime (x)$ from first principles if $f(x)=2x^2-1$ .	$(5)$
$7.2$	Determine:
$\quad 7.2.1$	$\frac{\displaystyle d}{\displaystyle dx}(\sqrt[5]{x^2}+x^3)$	$(3)$
$\quad 7.2.2$	$f^\prime (x)$ if $f(x)=\frac{\displaystyle 4x^2-9}{\displaystyle 4x+6}\:$ ; $x\neq -\frac{\displaystyle 3}{\displaystyle 2}$	$(4)$
		$\textbf{[12]}$