Using your answer from part c find dydx and d2ydx2 in terms

Question

Question: The position of a particle at time t is given by x = et + 3 and y = e^2t + 6e^t + 9.

(a) Find dy/dx in terms of t.

(b) Find d²y/dx². What does this tell you about the concavity of the graph?

(c) Eliminate the parameter and write y in terms of x.

(d) Using your answer from part (c), find dy/dx and d²y/dx² in terms of x. Show that these answers are the same as the answers to parts (a) and (b).