note that gradient = [tex]\frac{dy}{dx}[/tex] at x = a
calculate [tex]\frac{dy}{dx}[/tex] for each pair of functions and compare gradient
(a)
[tex]\frac{dy}{dx}[/tex] = 2x and [tex]\frac{dy}{dx}[/tex] = - 1
at x = 4 : gradient = 8 and - 1 : 8 > - 1
(b)
[tex]\frac{dy}{dx}[/tex] = 2x + 3 and [tex]\frac{dy}{dx}[/tex] = - 2
at x = 2 : gradient = 7 and - 2 and 7 > - 2
(c)
[tex]\frac{dy}{dx}[/tex] = 4x + 13 and [tex]\frac{dy}{dx}[/tex] = 2
at x = - 7 : gradient = - 15 and 2 and 2 > - 15
(d)
[tex]\frac{dy}{dx}[/tex] = 6x - 5 and [tex]\frac{dy}{dx}[/tex] = 2x - 2
at x = - 1 : gradient = - 11 and - 4 and - 4 > - 11
(e)
y = √x = [tex]x^{\frac{1}{2} }[/tex]
[tex]\frac{dy}{dx}[/tex] = 1/(2√x) and [tex]\frac{dy}{dx}[/tex] = 2
at x = 9 : gradient = [tex]\frac{1}{6}[/tex] and 2 and 2 > [tex]\frac{1}{6}[/tex]
