Problem with differentiation
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From: Albert on 6 Jun 2010 20:22 f(x) = (4x^2 - 1)^6, g(x) = (4x^2 - 1)^5 Find {x: f'(x)> g'(x)} f'(x) = 48x(4x^2 - 1)^5 g'(x) = 40x(4x^2 - 1)^4 Solve 48x(4x^2 - 1)^5 > 40x(4x^2 - 1)^4 48x(4x^2 - 1) > 40x 48(4x^2 - 1) > 40 6(4x^2 - 1) > 5 4x^2 - 1 > 5 / 6 4x^2 > 11 / 6 x^2 > 11 / 24 x^2 - 11 / 24 > 0 Solve x^2 - 11 / 24 = 0 x < (-1/2) * sqrt(11/6), x > (1/2) * sqrt(11/6) This doesn't match with the book's answer - what am I doing wrong?
From: porky_pig_jr on 6 Jun 2010 20:28 On Jun 6, 8:22 pm, Albert <albert.xtheunkno...(a)gmail.com> wrote: > f(x) = (4x^2 - 1)^6, g(x) = (4x^2 - 1)^5 > > Find {x: f'(x)> g'(x)} > > f'(x) = 48x(4x^2 - 1)^5 > g'(x) = 40x(4x^2 - 1)^4 > > Solve 48x(4x^2 - 1)^5 > 40x(4x^2 - 1)^4 > 48x(4x^2 - 1) > 40x > 48(4x^2 - 1) > 40 > 6(4x^2 - 1) > 5 > 4x^2 - 1 > 5 / 6 > 4x^2 > 11 / 6 > x^2 > 11 / 24 > x^2 - 11 / 24 > 0 > Solve x^2 - 11 / 24 = 0 > x < (-1/2) * sqrt(11/6), x > (1/2) * sqrt(11/6) > > This doesn't match with the book's answer - what am I doing wrong? doesn't look like you computed the derivatives correctly. Hint: chain rule.
From: porky_pig_jr on 6 Jun 2010 20:29 On Jun 6, 8:22 pm, Albert <albert.xtheunkno...(a)gmail.com> wrote: > f(x) = (4x^2 - 1)^6, g(x) = (4x^2 - 1)^5 > > Find {x: f'(x)> g'(x)} > > f'(x) = 48x(4x^2 - 1)^5 > g'(x) = 40x(4x^2 - 1)^4 > > Solve 48x(4x^2 - 1)^5 > 40x(4x^2 - 1)^4 > 48x(4x^2 - 1) > 40x > 48(4x^2 - 1) > 40 > 6(4x^2 - 1) > 5 > 4x^2 - 1 > 5 / 6 > 4x^2 > 11 / 6 > x^2 > 11 / 24 > x^2 - 11 / 24 > 0 > Solve x^2 - 11 / 24 = 0 > x < (-1/2) * sqrt(11/6), x > (1/2) * sqrt(11/6) > > This doesn't match with the book's answer - what am I doing wrong? Oops, sorry about that, I'm wrong, you computed the derivatives corectly.
From: Richard Henry on 6 Jun 2010 20:32 On Jun 6, 5:22 pm, Albert <albert.xtheunkno...(a)gmail.com> wrote: > f(x) = (4x^2 - 1)^6, g(x) = (4x^2 - 1)^5 > > Find {x: f'(x)> g'(x)} > > f'(x) = 48x(4x^2 - 1)^5 > g'(x) = 40x(4x^2 - 1)^4 > > Solve 48x(4x^2 - 1)^5 > 40x(4x^2 - 1)^4 > 48x(4x^2 - 1) > 40x > 48(4x^2 - 1) > 40 > 6(4x^2 - 1) > 5 > 4x^2 - 1 > 5 / 6 > 4x^2 > 11 / 6 > x^2 > 11 / 24 > x^2 - 11 / 24 > 0 > Solve x^2 - 11 / 24 = 0 > x < (-1/2) * sqrt(11/6), x > (1/2) * sqrt(11/6) > > This doesn't match with the book's answer - what am I doing wrong? What's the book's answer?
From: Albert on 6 Jun 2010 20:42
Richard Henry wrote: > What's the book's answer? {x: x > sqrt(66) / 12) U {x: -sqrt(66) / 12 < x < -1/2} U {x: -1/2 < x < 0} |