EE 231_B1
Damir Iraliyev
1246540
Homework#5:
Question7.4
Given a function
= .
+
+
fx
1 5x6 2x4 12x
a)
Plot the function
b)
Use analytical Methods to prove that the function is concave
for all values
of ‘x’
c)
Differentiate the function and then use rootlocation method to solve for the
maximum f(x) and corresponding value of ‘x’
Solution:
a)
For Graph of
f(x)
please refer to the back of this report. Thank you.
b)
A continuous function is said to be concave if and only If a function always bears
negative results for second derivative of the function therefore the function is concave:
We check and see:
= .
+
+
fx
1 5x6 2x4 12x
=
+
+
f'x
9x5 8x3 12
=
+
f''x
45x4 24x2
As we can clearly see from f’’(x) that the function is always negative for all
values of x because of the x^4 and x^2 and the fact that 45>24. QED
c)
First derivative of the function is:
=
+
+
f'x
9x5 8x3 12
And
=
+
f''x
45x4 24x2
Then we use NewtonRaphson Method to locate the root of the function since we
positively know that the function is convergent?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 Vorobyov
 Derivative, 1%, 4%, 0.4%, Use analytical Methods

Click to edit the document details