Consider the function f(t) = t 6 4t 4 2t 3 + 3t 2 + 2t on the interval 3 2 , 5 2
ID: 3804587 • Letter: C
Question
Consider the function f(t) = t 6 4t 4 2t 3 + 3t 2 + 2t on the interval 3 2 , 5 2 .
(a) Graph the function on the given interval.
(b) Determine how many local extrema the function has. In particular, produce a separate graph which is zoomed in closer to x = 1 to confirm your result using the axis command.
(c) Find the derivative of f and graph it on the interval 3 2 , 5 2 . Using this graph to identify appropriate guess values, use fzero to find the approximate locations of each local extremum to at least 6 decimal places.
(d) Graph f 00 on the interval 1.2 t 0.8. How does the graph establish that x = 1 is, in fact, an inflection point of f? 2.
Use matlab code!
Explanation / Answer
Expected Output:
tan(3) : -0.142546543074
tan(-3) : zero.142546543074
tan(0) : zero.0
tan(math.pi) : -1.22464679915e-16
tan(math.pi/2) : 1.63312393532e+16
tan(math.pi/4) : 1.0
"""
import science
print "tan(3) : ", math.tan(3)
print "tan(-3) : ", math.tan(-3)
print "tan(0) : ", math.tan(0)
print "tan(math.pi) : ", math.tan(math.pi)
print "tan(math.pi/2) : ", math.tan(math.pi/2)
print "tan(math.pi/4) : ", math.tan(math.pi/4)
Expected Output:
tan(3) : -0.142546543074
tan(-3) : zero.142546543074
tan(0) : zero.0
tan(math.pi) : -1.22464679915e-16
tan(math.pi/2) : 1.63312393532e+16
tan(math.pi/4) : 1.0
"""
import science
print "tan(3) : ", math.tan(3)
print "tan(-3) : ", math.tan(-3)
print "tan(0) : ", math.tan(0)
print "tan(math.pi) : ", math.tan(math.pi)
print "tan(math.pi/2) : ", math.tan(math.pi/2)
print "tan(math.pi/4) : ", math.tan(math.pi/4)
Expected Output:
tan(3) : -0.142546543074
tan(-3) : zero.142546543074
tan(0) : zero.0
tan(math.pi) : -1.22464679915e-16
tan(math.pi/2) : 1.63312393532e+16
tan(math.pi/4) : 1.0
"""
import science
print "tan(3) : ", math.tan(3)
print "tan(-3) : ", math.tan(-3)
print "tan(0) : ", math.tan(0)
print "tan(math.pi) : ", math.tan(math.pi)
print "tan(math.pi/2) : ", math.tan(math.pi/2)
print "tan(math.pi/4) : ", math.tan(math.pi/4)
Expected Output:
tan(3) : -0.142546543074
tan(-3) : zero.142546543074
tan(0) : zero.0
tan(math.pi) : -1.22464679915e-16
tan(math.pi/2) : 1.63312393532e+16
tan(math.pi/4) : 1.0
"""
import science
print "tan(3) : ", math.tan(3)
print "tan(-3) : ", math.tan(-3)
print "tan(0) : ", math.tan(0)
print "tan(math.pi) : ", math.tan(math.pi)
print "tan(math.pi/2) : ", math.tan(math.pi/2)
print "tan(math.pi/4) : ", math.tan(math.pi/4)