# Find the two real roots of |x3|+x −6=0 using the MATLAB function fnewton.

Use the MATLAB function fnewton to ﬁnd a root of

x1.4−√x+1/x−100=0

given an initial approximation 50. Use an accuracy of 10−4. Find the two real roots of |x3|+x −6=0 using the MATLAB function fnewton. Use initial approximations−1 and 1 and an accuracy of 10−4. Plot the function using MATLAB to verify that the equation has only two real roots. Hint: Take care in ﬁnding the derivative of the function. Explain why it is relatively difﬁcult to ﬁnd the root of tanx−c=0 when c is a large. Use the MATLAB function fnewton, with initial approximations 1.3 and 1.4 and accuracy 10−4, to ﬁnd a root of this equation when c=5 and c=10. Compare the number of iterations required in both cases. Hint: A MATLAB plot will be useful.

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