South Black

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These are questions asked by south

Write a Maple procedures called “biggest4” and “smallest4” to find
a) the biggest
b) the smallest
of the given numbers  a = -1/3, b = 0, c = 7/3, d = -2

i guess i need to use end proc for programing but i dont understand:

i need to use two different methods to solve the initial value problem. I tried but didnt find the answer 

y" + 4y' + 4y = sin(x), y(0) = 1 , y'(0) = 0

y" + 4*diff(y(x), x) + 4*y(x) = sin(x)

dsys1 := {diff(y(x), x, x) + diff(y(x), x) + 4*y(x) = sin(x), y(0) = 1, D(y)(0) = 0};
dsol1 := dsolve(dsys1, numeric, method = gear);

 y = ax^3 + bx^2 + cx + d this is curve and is passing through the points (−1,−4),(1,0),(2,0),(3,−4).
1) Find the values of 𝑎,𝑏,𝑐 and 𝑑.
2) Plot the curve and the points given on the same axis.

I tried solving with derivative of the curve but i didnt find the exact values.

Let the curves y=2x^3-x^2-5x   and 𝑦=−𝑥^2+3𝑥be given.
a) Plot both curves on the same 𝑥y −axis.
b) Shade the region (between the curves).
c) Calculate the area of the region enclosed by the curves given.

What values of a and b make f(x)=x³+ax²+bx have

a. A local maximum at x=−1 and a local minimum at x=3?

b. A local minimum at x=4 and a point of inflection at x=1?

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