1) A car speeding around a curve in the shape y =x/1+x^2 skids off at the point (1/2, 2/5). If the car continues in a straight path will it hit a tree located at the point (3,8/5)?
2) Determine the numbers a, b, and c such that the graph of y=x^3 + ax^2 + bx + c satisfies the following three conditions:
(i) it has a horizontal tangent line at x = -1, and
(ii) its tangent line at x=1 is parallel to the line y=8x-5,and
(iii) it passes through the point (1, 2).
please show step by step
2) Determine the numbers a, b, and c such that the graph of y=x^3 + ax^2 + bx + c satisfies the following three conditions:
(i) it has a horizontal tangent line at x = -1, and
(ii) its tangent line at x=1 is parallel to the line y=8x-5,and
(iii) it passes through the point (1, 2).
please show step by step