Please answer 1(a-e) thanks! ho122321. Consider the curve in parametric form x(t) = t³ - 3ta) Find the point(s) where the tangent line to the curve is horizontaly(t) = 3t² - 9b) Find the point(s) where the tangent line to the curve is verticalc) Find the points where there are more than one tangent line and find the equations of those linesd) Determine the values of t for which the curve in concave up or concave downe) Sketch the graph of the curve on the x- y- plane$3=(1)x ) hommen al evonorl syad) of bull magnet adrovei ovurd of enllagrost odlqu ovsomo)0 VND 5 toyd novig zi vomit te ploiting ooo to notizo3200 S = C2. Repeat the problem about the collision points discussed in recitation but this time describe what happens itthe second particle is given instead bynia.x₂ = 3 + costru wol y₂ = 1 + sin tuolo 0≤t≤ 2πoy) esloineq diod to a11 Tomilomes aft is only one sa ove stoine di o.o.I fainioq notillos noitesersta

According to the guidelines, only three subpart can be answered. Please repost other question separately. The given curve is x=t3-3t, y=3t2-9. The objectives are to calculate the points where the tangents are horizontal or vertical. The power rule of differentiation states that d dttp=ptp-1, where p is any real number. Differentiate the expression of x,y by the power rule of differentiation to obtain the expression of dxdt, dydt. x=t3-3tdxdt=d dtt3-3t=3t2-3dydt=d dt3t2-9=3(2t)-0=6t The tangent line is horizontal if dydx=0, i.e. dydt=0. Equate the expression of dydt with 0 and simplify to calculate the value of t. dydt=06t=0t=0 Substitute t=0 in the expression of x,y and simplify to calculate the point. x=03-3×0=0y=3×02-9=-9 Hence, the point 0,-9 is the point where the tangent line is horizontal.The tangent line is vertical if dxdy=0, i.e. dxdt=0. Equate the expression of dydt with 0 and simplify to calculate the value of t. dxdt=03t2-3=0t2=1t=±1 Substitute t=±1 in the expression of x,y and simplify to calculate the point. x=13-3×1=-2y=3×12-9=-6x=(-1)3-3×(-1)=2y=3×(-1)2-9 =-6 Hence, the points -2,-6, (2,-6) are the points where the tangent line is horizontal. The graph of the given curve is