Search over 10,000 free study notes

This requires use of the quotient rule: d/dx[f(x)/g(x)] = [g(x)f'(x) - g'(x)f(x)]/[g(x)^2]dy/dx = ([(3x-1)*2x] - 3x^2)/[(3x-1)^2],= (3x^2-2x)/[(3x-1)^2],=[x(3x-2)]/[(3x-1)^2]

y = x³ - 3x² - 24x + 5, First, calculate the derivative of y and find its roots when y = 0:dy/dx = 3x² - 6x -24 = 0 -> x² - 2x - 8 = 0 -> (x+2)(x-4) = 0Th...

512

Use the formula: ∫uv' dx = uv - ∫u'v dx (use I = the integral we're looking for)Note we cant integrate ln x easily but we can differentiate into 1/x so we use:u = ln x and v' = x we have u' = 1/x and v =...

y = 3x -2(3x-2)² - x - 6x² = 0 9x²- 12x + 4 - x - 6x² = 03x² - 13x + 4 = 0(3x - 1)(x-4) = 0 x = 1/3 or x = 4then y = -1 when x = 1/3 and y = 10 for...