Question

Can someone check this please? - Differentiation and Maximum points

Answer 1

(a) (i) Given that \[y = x+1+\frac{ 4 }{ x^2 }\], find dy/dx

Answer 2

(a) (ii) Find the coordinates of the minimum point M

Answer 3

ok what have you gotten for ai?

Answer 4

just so you know you can write ai as:
\[\text{ find } \frac{dy}{dx} \text{ given } y=x+1+4x^{-2}\]

Answer 5

dx/dx=1
dc/dx=0 where c is a constant
the third term you need power rule

Answer 6

dy/dx=1-8/x=0 for max or min
x=8
y=8+1+4/64 and solve
does this help?

Answer 7

\[\frac{dy}{dx}=1-\frac{8}{x^3}=\frac{x^3-8}{x^3}\]
set this to zero
\[x^3-8=0 \Longrightarrow (x-2)(x^2+2x+4)=0\]

Answer 8

solve from there