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 February 18th, 2019, 08:48 PM #1 Member   Joined: Feb 2018 From: Iran Posts: 52 Thanks: 3 Graph of a function The graph of the function f(x) = a(x– 2)^2(x+ b) is shown in the figure.Find a and b. I solved this question by plugging f(2)=0 then I get b=-2 Then I plugged f(0)=3 and i found a but answer is not true according to my book why is this so?? February 18th, 2019, 09:10 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,529 Thanks: 1389 $f(2)=0$ regardless of what the value of $b$ is. Do you see why? How about if we note that $f(0)=3$ $4ab = 3$ They then seem to be trying to indicate that the maximum of $f(x)$ occurs at $x=3$ If this is the case then the first derivative of $f(x)$ will be equal to $0$ at $x=3$ $\dfrac{df}{dx} = 2a(x-2)(x+b) + a(x-2)^2 = (x-2)(2a(x+b)+a(x-2))$ $2a(x+b)+a(x-2) = 0 ~@x=3$ $2a(3+b) + a(3-2) = 0$ $6a+2ab+a = 0$ $a(7+2b)=0$ $a=0$ or $b = -\dfrac{7}{2}$ $a \neq 0$ as $4ab=3$ from above so $b = -\dfrac{7}{2}$ $4 a \left(-\dfrac{7}{2}\right) = 3$ $-14a = 3$ $a = -\dfrac{3}{14}$ February 18th, 2019, 10:13 PM   #3
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Quote:
 Originally Posted by romsek They then seem to be trying to indicate that the maximum of $f(x)$ occurs at $x=3$
This should read they seem to be trying to indicate that there is a local maximum of $f(x)$ at $x=3$ Tags function, graph Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post idontknow Calculus 1 January 13th, 2019 08:42 AM hy2000 Algebra 2 August 14th, 2018 12:02 AM hy2000 Algebra 7 August 13th, 2018 11:45 PM safyras Algebra 1 January 2nd, 2012 12:22 PM mikeportnoy Algebra 3 March 10th, 2009 06:35 AM

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