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[Petinga]

I need the solution to this question if anyone can help


1. Consider the curve y=7 + 4x^3 - 3x^4

i) Find the coordinates of the two stationary points
ii) find all values for which second derivative=0
iii) Determine the nature of the stationary points

 

[香港!]

I need the solution to this question if anyone can help


1. Consider the curve y=7 + 4x^3 - 3x^4

i) Find the coordinates of the two stationary points
ii) find all values for which second derivative=0
iii) Determine the nature of the stationary points

i)y=7 + 4x^3 - 3x^4
y'=12x²-12x³=12x²(1-x)
y''=24x-36x²
Now Set y'=0, i.e:
12x²(1-x)=0
.: x=0 or x=1
.: the coordinates of the two stationary points are;
(0, sub that into ur y=...)
(1, sub that into ur y=...)
ii) Set y''=0
so 24x-36x²=0
x(24-36x)=0
.: x=0 or x=24\36=..
are the values for which second derivative=0
iii) To determine the 'nature', put ur stationary points in ur y'' to see if it's +VE or -VE .. etc..