Question

3. Consider the function 4 242 where bE R. Use MATLAB to (a) Define t and b as symbolic variables. (b) Create the symbolic function A. (c) Find A'(t). See section 1.9.1 of the MATLAB Manual) (d) Solve A'(t)0. (See section 1.9.3 of the MATLAB Manual.) (e) Find A(0), A(b/v2) and A(b). (Use subs (A,0))

Answer 1

From the outputs,it is clear that critical points (A'(t)=0) that lies in the given interval are 0 and   .So we need to check only these points and endpoints,which is what we did in (e). From the output we find that minimum value occurs at   . The code is attached below.

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clear all
syms t b A(t)%We declare symbolic variables t,b and function A(t)
A(t)=t^4-(b^2*t^2);%Definition of A(t)
dA=diff(A)%dA=derivative of A

roots=solve(dA,t) %Solving for A'(t)=0

%Next lines displays results after substitution
%Only sub is required for substutuion but to display
%using disp we need to convert syms to char,hence the char
disp(['A(0) = ', char(subs(A,0))]);
disp(['A(b/2^1/2) = ', char(subs(A,b/2^1/2))]);
disp(['A(b) = ', char(subs(A,b))]);
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