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Firstly, find the values of x where f'(x) = 0
f'(x) = 6x2 - 54
6x2 - 54 = 0
6(x+3)(x-3) = 0
x = 3, y = -108 and x = -3, y =...
We know that when f(x) = x^n, f'(x) = nx^n-1 (1)
So we apply this to all components of f(x), giving
f'(x) = 2(3x) + 7 = 6x +...
In order to find the area bounded by a curve and the horizontal axis, we must integrate the curve between the specified limits.
Firstly we must integrate the curve x^2-2x+3. To integrate ...
At the point where the line crosses the x axis, y=0
3x^2+7x-6=0
(3x-2)(x+3)=0
3x-2=0 or x+3=0
giving x=2/3 and x=-3
so the line cro...
use the chain rule on the y^2 term to get 2y*(dy/dx)
hence the overall solution is 2x + 2y*(dy/dx)
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