(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1. The line perpendicular to the curve y = 2x^3 - x^2 + x - 3 at the point (1, -1) will intersect the x-axis at what point?

2. f(x) = |x^2 - 5| - x, for all x. Let g = f(f(f(x))), find g'(2). I tried just subbing in 2x - 1, the first derivative, to f(2x - 1) and then once more and ended up with 16 somehow, when the answer is -45.

3. If f(x) = ln(2X^2 + x - 1) - ln(x+1) find the 98th derivative at (1/2 + sqrt(2)/2). I know that the derivative simplifies to 2(2x - 1) and the 2nd derivative to -2/(2x-1)^2 and the 3rd to -8(2x-1)/2x-1)^4 but I always have a hard time generalizing these and then getting the answer (especially because the answer is -2^49(97!) and I have no idea how the factorial gets worked in.

2. Relevant equations

y1 - y0 = m(x1 - x0)

3. The attempt at a solution

Finding the derivative and subbing in x = 1 gives a slope of 5 at the point specified, which means m = -1/5. When solved this gives x = -10, however the correct answer is apparently -4.

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# Homework Help: Derivatives: Composites, normal lines, n-th derivatives and more.

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