(1) Input function F(X) from your online assignment 1 (Bisection) to Matlab by using handles to functions of functions like function h below.

f = @(x) x.^2;

g = @(x) 3*x;

h = @(x) g(f(x));

h(3)

ans = 27

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F(X) From Question one:

A=(X + 0.33) / 4.29 B=(X - 3.96) / 4.29 P1=((A-1)**2)*(1+2*A) P2=((B+1)**2)*(1-2*B) F(X) = (P1 * 2.04) + (P2 * (-7.89) ) 

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(2) Plot (X, F(X)) so we can see all three roots.

(3) Choose three pairs of Xl and Xu from your figure and use

options=optimset(display, iter);

fzeor(F, [Xl Xu], options)

to find the three roots. Check if they are correlated with the roots in your figure.

(4) Find the first, second, third and fourth derivative functions of F(X) from (1) by using diff (see below):

diff -- differentiate symbolic expression or function

Syntax and Description:

diff(F,var)-- differentiates F with respect to the variable var.

diff(F,var,n)-- computes the nth derivative of F with respect to the variable var.

Examples:

Find the derivative of the function sin(x^2).

syms f(x)

f(x) = sin(x^2);

df = diff(f,x)

df(x) =

2*x*cos(x^2)

Find the value of the derivative at x = 2.

Convert the value to double.

df2 = df(2)

df2 =

4*cos(4)

double(df2)

ans =

-2.6146

Higher-Order Derivatives of Univariate Expression

Find the 4th, 5th, and 6th derivatives of this expression:

syms t

d4 = diff(t^6,4)

d5 = diff(t^6,5)

d6 = diff(t^6,6)

d4 =

360*t^2

d5 =

720*t

d6 =

720

Input Arguments

F Expression or function to differentiate, specified as a symbolic expression or function or as a vector or matrix of symbolic expressions or functions. If F is a vector or a matrix, diff differentiates each element of F and returns a vector or a matrix of the same size as F.

var Differentiation variable, specified as a symbolic variable.

n Differentiation order, specified as a non-negative integer.