Final answer:
To find points on the interval [-5,5] where the tangent to y=xcosx is parallel to the secant line, find where their slopes are equal. Hence, none of the options are correct.
Step-by-step explanation:
To find the points on the interval [-5,5] where the tangent to the curve y=xcosx is parallel to the secant line, we need to find where the slopes of the tangent and secant lines are equal. The slope of the secant line is equal to the difference in y-coordinates divided by the difference in x-coordinates between two points.
Since the secant line is parallel to the tangent line, their slopes will be equal. The slope of the tangent line can be found by taking the derivative of the function y=xcosx, which is given by the product rule: dy/dx=cosx-xsinx.
Set this derivative equal to the slope of the secant line and solve for x to find the points of tangency. In this case, there are old{2} points on the interval [-5,5] where the tangent is parallel to the secant line.