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At x = 1... y(1) = 0. Via differentiation, we have... dy/dx = 1 - 2x For x = 1... dy/dx = 1 - 2 = -1 So... y = -1(x - 1) The equation of the normal line is... y = x - 1 Determine the solutions of x, given the equation of the normal line...

1 Answers · Science & Mathematics · 17/02/2013

at x=3, f(x)=5, with a slope of 1.1. So, f(x)=mx+b, 5=1.1(3)+b --> b = 5-3.3 = 1.7 f(x) = 1.1x+1.7 at x=3 g(x) = -4 with a slope of 0.7 g(x) = mx+b, -4 = 0.7(3)+b --> b=-4-2.1 = -6.1 g(x) = 0.7x - 6.1 f(x)*g(x) = (1.1x+1.7)(0.7x-6.1) = .77x^2-5.52x-10.37 [f(x)*g(x)]' = 1.54x-5.52 @x=3: 1.54(3)-5.52 = 4.62-5.52 = -0.9

1 Answers · Science & Mathematics · 11/02/2013

√(x + y) +√(x - y) = 4 (1 + dy/dx) / (2√(x + y)) + (1 - dy/dx) / (2√(x - y)) = 0 dy/dx = 2 .... at (5,4) , i.e. 3/6 - 1/2 = 0 Answer: 2

1 Answers · Science & Mathematics · 17/02/2013

Assume the lines intersect the parabola at the point (x, x^2 + x). It then follows that: dy/dx = 2x + 1 = (x^2 + x + 3)/(x - 2) 2x^2 - 3x - 2 = x^2 + x + 3 x^2 - 4x - 5 = 0 (x - 5)(x + 1) = 0 x = 5, -1

1 Answers · Science & Mathematics · 10/02/2013

f(0) = 1, ===.===> y-intercept = 1 f’(0) = 2, ======> y is increasing at x = 0 f’’(0) = 0, ===-==> possibly an inflection point at x = 0 A) No. Even if one of the conditions required for an inflection point is given, i.e f’’(0) = 0, no other...

1 Answers · Science & Mathematics · 18/05/2016

lim h-> 0 of ((x+h)^3-(x^3))/h = lim h-> 0 ((2+h)^3-(2^3))/h since if you plug in 0 for h, you'll get the expression 0/0, you can use l'Hopital's rule that if you have infinity over infinity limit, you can take derivatives of top and bottom (each separately, this is not the quotient rule) to simplify the expression...

1 Answers · Science & Mathematics · 02/04/2009

I'm assuming that your difficulty comes from the setting up of the problem, not from setting derivatives = 0. Let: x = length going to shape a rectangle, and (30 - x) = length going to shape a square Area of square = [ (30 - x) / 4 ]^2...

1 Answers · Science & Mathematics · 06/10/2008

Part 1:If you mean the formula with n-1 in the denominator (known as Bessel correction formula-this is the most common formula and is usually called "sample standard deviation") then the conditions are that the variables in the sample...

3 Answers · Science & Mathematics · 22/04/2011

I am a high school math teacher. This question is from the 2011 AB exam and a calculator was allowed for this question. You are correct to be thinking about integrating this, but you don't have to do it "by hand."...

2 Answers · Science & Mathematics · 25/04/2013

Each operation has an opposite for solving equations. Just work through the equation, from the outside in, until you have your solution: x = answer (formula with a,b,c,d, and p) Some examples of opposites are...

4 Answers · Science & Mathematics · 09/11/2011

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