simple differentiation question (1 Viewer)

[apak]

to find the stationary points for y = (3x-1)(x-2)^4
isit essential to differentiate then expand the whole thing out. then testing for a factor then using long division?
can som1 put solution up please? thx in adv

 

[PLooB]

Use product rule:

y' = 3(x-2)⁴ + 4(3x-1)(x-2)³

this simplifies to

= 5(x-2)³(3x-2)

when y' = 0, x = 2 or 2/3

 

[Riviet]

The product rule is the quickest and easiest way to differentiate this equation because (x-2)⁴ would take forever to expand and would therefore be a waste of time. You will also need to use the chain rule on (x-2)⁴ in addition to the product rule for the whole expression.