Question

Can someone explain this differentiation question to me? I can differentiate but then I'm not sure what I am doing

Answer 1

note that gradient = $\frac{dy}{dx}$ at x = a

calculate $\frac{dy}{dx}$ for each pair of functions and compare gradient

(a)

$\frac{dy}{dx}$ = 2x and $\frac{dy}{dx}$ = - 1

at x = 4 : gradient = 8 and - 1 : 8 > - 1

(b)

$\frac{dy}{dx}$ = 2x + 3 and $\frac{dy}{dx}$ = - 2

at x = 2 : gradient = 7 and - 2 and 7 > - 2

(c)

$\frac{dy}{dx}$ = 4x + 13 and $\frac{dy}{dx}$ = 2

at x = - 7 : gradient = - 15 and 2 and 2 > - 15

(d)

$\frac{dy}{dx}$ = 6x - 5 and $\frac{dy}{dx}$ = 2x - 2

at x = - 1 : gradient = - 11 and - 4 and - 4 > - 11

(e)

y = √x = $x^{\frac{1}{2} }$

$\frac{dy}{dx}$ = 1/(2√x) and $\frac{dy}{dx}$ = 2

at x = 9 : gradient = $\frac{1}{6}$ and 2 and 2 > $\frac{1}{6}$