Question-2;
Consider the function f(x)= -cos3x -4sin3x.
(a)Find the equation of the line normal to the graph of f(x) when x= pie/6 .
(b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal.
(c)Find the absolute extrema of the function f(x)=5+6x^3-3x^4 on the interval [-2,2] .
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Question-3: Consider the two parabolas :y1=2x^2-3x-1 and y2=x^2+7x+20.
(a) Find the points of intersection of the parabolas and decide which one is greater than the other between the intersection points.
(b) Compute the area enclosed by the two parabolas.
(c) Use Mathcad to draw the graphs of the parabolas and find their intersection points graphically .
(d) Solve the differential equation dy/dx = -exp(5-x)+3/5x^2 ; y(5)=3
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