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dy/dx = 6x2 + 4x + 9
dy = (6x2 + 4x + 9) dx
integrating gives:
y= (6x3/3) + (4x2/2) + 9x + c
y= 2x3 + 2x2 + 9...
6x^2 + 5x +7 =y
dy/dx = 12x + 5
To solve for a point of inflection:
dy/dx = 12x + 5 = 0
x=-5/12
y=143/24
The general form of a quadratic equation is, ax2 +bx + c = 0. If we divide all terms by a we get, x2 +(b/a)x + c/a = 0. then by completing the square we get (x+(b/2a))2 + ...
Just because a function is continuous at a point, that doesn't mean it has a derivative at that point. If a function is differentiable on an interval, then it is continuous on that interval, but the rever...
When rationalising, multiply the fraction by the denominator - so what that means is multiply the fraction by the square rooted number over the square rooted number. The numerators then multiply to give 6...
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