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# A2 Maths C3- Differentiation watch

1. The volume of a cone is given by
given that L is constant and x varies find the maximum value of v in terms of L and
2. Isn't this just a C2 question with C3 differentiation? If you know how to differentiate V and solve V' = 0 then you'll get the answer in no time.
3. (Original post by shawn_o1)
Isn't this just a C2 question with C3 differentiation? If you know how to differentiate V and solve V' = 0 then you'll get the answer in no time.
Product rule is required (C3).

What have you tried so far OP?
4. does dy/dx=
5. (Original post by AlexS101)
does dy/dx=

it says that L is constant so you don't have to treat it as a variable. you have to use the product rule. you have cos(x)(sin(x))^2, so the differential is 2cos(x)sin(x)cos(x) -sin^3(x) =0

when sin(x) = 0 then x =0 so that means there is no volume as it is the minimum solution.
that leaves you with 2cos^2(x)-sin^2(x)=0
re-arange to either get
cos(x)=1/sqrt(3)
or
tan(x) = sqrt(2)
or
sin(x) = sqrt(2/3)
subbing this back into the formula for V, V(max) = (pi/3)(L^3)(2/3sqrt(3))

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