## Symbolic math toolbox for use with MATLAB - user's guide by MathWorks

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5 −4 Global minima −6 −4 −2 0 x 2 4 6 The foregoing analysis confirms part of our original guess that the range of f''(x) is [-4, 1]. We can confirm the other part by examining the fourth zero of f'''(x) found by solve. First extract the fourth zero from z and assign it to a separate variable s = z(4) to obtain s = atan((–255+60*19^(1/2))^(1/2)/(10–3*19^(1/2)))+pi Executing sd = double(s) displays the zero’s corresponding numeric value. 4483 1-41 1 Tutorial Plotting the point (s, f2(s)) against f2, using M1 = double(subs(f2,x,s)); plot(sd,M1,'ko') text(-1,1,'Global maximum') visually confirms that s is a maximum.

F simplify(f) x∗(x∗(x–6)+11)–6 x^3–6∗x^2+11∗x–6 (1–x^2)/(1–x) x + 1 (1/a^3+6/a^2+12/a+8)^(1/3) ((2*a+1)^3/a^3)^(1/3) syms x y positive log(x∗y) log(x) + log(y) exp(x) ∗ exp(y) exp(x+y) besselj(2,x) – ... 2*besselj(1,x)/x + besselj(0,x) 0 gamma(x+1)–x*gamma(x) 0 cos(x)^2 + sin(x)^2 1 simple The simple function has the unorthodox mathematical goal of finding a simplification of an expression that has the fewest number of characters. Of course, there is little mathematical justification for claiming that one expression is “simpler” than another just because its ASCII representation is shorter, but this often proves satisfactory in practice.

The command format; % Default format of 5 digits zr = double(z) 1-36 Calculus converts the zeros to double form. 4483 So far, we have found three real zeros and two complex zeros. However, a graph of f3 shows that we have not yet found all its zeros. '); title('Zeros of f3') Zeros of f3 3 2 1 0 −1 −2 −3 −6 −4 −2 0 x 2 4 6 1-37 1 Tutorial This occurs because f'''(x) contains a factor of sin(x), which is zero at integer multiples of π. The function, solve(sin(x)), however, only reports the zero at x = 0.