My Math Forum Maximum and Minimum Turning Points

 Calculus Calculus Math Forum

 April 9th, 2013, 11:20 AM #1 Senior Member   Joined: Sep 2011 Posts: 395 Thanks: 0 Maximum and Minimum Turning Points This question is similar to one I posted yesterday. I have found d, but I'm unsure regarding the remaining values. Can anyone help? Many thanks. Q. The function $f(x)=ax^3+bx^2+cx+d$ has a max point at (0, 4) and a point of inflection at (1, 0). Find the values of a, b, c & d. Attempt: $4=a(0)^3+b(0)^2+c(0)+d$...(when (x, y) = (0, 4)$\rightarrow d=4$ $f'(x)=3ax^2+2bx+c\rightarrow3a(0)^2+2b(0)+c= 0$...(when x = 0)$\rightarrow c=0$ $f''(x)=6ax+2b=3ax+b\rightarrow3a(1)+2b=0$...(when x = 1, via point of inflection (1, 0))$\rightarrow b=-3a$ $f(x)=ax^3+bx^2+cx+d\rightarrow 4=a(1)^3-3a(1)^2+0(1)+4\rightarrow a-3a=0\rightarrow-2a=0\rightarrow a=0$ Ans.: (From text book): a = 2, b = -6, c = 0, d = 4.
 April 9th, 2013, 11:35 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,882 Thanks: 1088 Math Focus: Elementary mathematics and beyond Re: Maximum and Minimum Turning Points Correct up to your last line. a - 3a + 4 = 0, -2a = -4, a = 2.
 April 9th, 2013, 11:51 AM #3 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: Maximum and Minimum Turning Points [color=#000000]$f(x)=ax^3+bx^2+cx+d$, $f'(x)=3ax^2+3bx+c$, $f''(x)=6ax+3b$. $f(0)=4\Leftrightarrow d=4$ $f'(0)=0\Leftrightarrow c=0$ $f''(0)=0\Leftrightarrow 6a+2b=0\Leftrightarrow 3a+b=0$(1) $f(1)=0\Leftrightarrow a+b+4=0$(2) From (1) and (2) we get a=2 and b=6.[/color]
 April 9th, 2013, 12:43 PM #4 Senior Member   Joined: Sep 2011 Posts: 395 Thanks: 0 Re: Maximum and Minimum Turning Points Thanks again.

 Tags maximum, minimum, points, turning

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post bilano99 Calculus 2 August 7th, 2013 10:08 AM bilano99 Calculus 2 April 8th, 2013 12:15 PM Tutu Calculus 2 April 13th, 2012 07:39 AM harry buckle Algebra 7 January 25th, 2012 07:16 PM lemon Calculus 12 February 16th, 2010 10:08 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top