Considerthecurvex(t)=t2,y(t)=t3 −3t,for−∞<t<∞. 2 (a) Find all t that give x intercepts and y-intercepts, and plot them....

Considerthecurvex(t)=t2,y(t)=t3 −3t,for−∞<t<∞. 2

(a) Find all t that give x intercepts and y-intercepts, and plot them.

(b) Find all t which give horizontal or vertical tangents, and plot the corresponding points, with a short horizontal or vertical segment to indicate the tangent line.

(c) Find the values of t for which x(t) is increasing and those for which it is decreasing. Do the same for y.

(d) Determine what happens to x(t) and y(t) as t → ∞.

(e) Make a neat, careful sketch of the graph on the axes above. Use arrows which indicate the direction, and label all important values of t. Your graph must be consistent with the information in parts (a)-(d).

Expert Solution

milcah answered 2 years ago

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Question

Considerthecurvex(t)=t2,y(t)=t3 −3t,for−∞<t<∞. 2 (a) Find all t that give x intercepts and y-intercepts, and plot them....

Solutions

Expert Solution

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