1. Show that the curves y = x^3 - 3x + 4 and y = 3(x^2 - x) are tangent to each
ID: 2837468 • Letter: 1
Question
1. Show that the curves y = x^3 - 3x + 4 and y = 3(x^2 - x) are tangent to each other. That is, that there is point where the curves intersect and at this point the tangent lines to both curves are the same. 2. Find a parabola with the equation y = ax^2 + bx + c, that has a slope 4 at x = 1, slope -8 at x = ?1, and that passes through the point (2, 5). (i.e. you need to find the values of constants a, b, c such that all the conditions are satisfied.) 3. The position of an object at any time t is given by: s(t) = 3t^4 - 44t^3 + 108t^2 + 20. (a) Determine the velocity of the object at time t. (b) Does the object ever stop, i.e. does it ever have zero velocity? If so, find the times at which its velocity is zero. (c) When is the object moving to the right and when is the object moving to the left?Explanation / Answer
1)_---------->> Find the points of intersection of the two curves.
y = x
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