Parabolas : Concave up or Concave Down?

What does a parabola open upward and when does it open downward? Please give an example.

Use the Monotonocity Theorem to determine where the given function is concave up and where it is concave down. F(x) = (x - 1) / (x^2)

#4 What happens to concavity when functions are added? a) If f(x) and g(x) are concave up for all x, is f(x) + g(x) concave up for all x? Yes b) If f(x) is concave up for all x and g(x) is concave down for all x, what can you say about the concavity of f(x) + g(x)? For example, what happens if f(x) and g(x) are both polyn

1. Draw a sign graph to determine where the following function is increasing or decreasing. Identify all stationary points. y=2x^4-4x^2+1 2. Find the intervals where the following curve is concave up or down. Also find the coordinates of any points of inflection. y=2x^3 - x^2 +3x+5 3

1.) Find and equation of the tangent to the curve at the point corresponding to the given value of the parameter x= cos t + sin 2t, y= sin t + cos 2t (t=0) 2.) Find dy/dx and d^2/dx^2 for which values of t is the curve concave upward x= t + ln t, y = 1 - ln t

Let f(x)=x^(4)â?'6x^(3)+12x^(2). Find (a) the intervals on which f is increasing, (b) the intervals on which f is decreasing, (c) the open intervals on which f is concave up, (d) the open intervals on which f is concave down, and (e) the x-coordinates of all inflection points. (a) f is increasing on the interval(s) = (b)

This problem deals with lenses, please explain using equations, and ray diagrams. A real object is at the zero end of the meter stick. A large concave mirror at the 100-cm end of a meter stick forms an image of the object at the 70-cm position. A small convex mirror placed at the 20-cm position forms a final image at the 10-c

Which kind of spherical mirror, concave or convex, can be used to start a fire with sunlight? For the best results, how far from the mirror should the paper to be ignited be placed?

I am taking a course by distance, and my professor provided an example of how to create a Hessian matrix using partial derivatives. He gave another example that just had the solution for us to try on our own. I think that I am somehow not taking the second order partial derivative right. The attached file has the professor