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February 18th, 2019, 08:48 PM  #1 
Member Joined: Feb 2018 From: Iran Posts: 44 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: 2,427 Thanks: 1314 
$f(2)=0$ 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 $x=3$ $\dfrac{df}{dx} = 2a(x2)(x+b) + a(x2)^2 = (x2)(2a(x+b)+a(x2))$ $2a(x+b)+a(x2) = 0 ~@x=3$ $2a(3+b) + a(32) = 0$ $6a+2ab+a = 0$ $a(7+2b)=0$ $a=0$ 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 
Senior Member Joined: Sep 2015 From: USA Posts: 2,427 Thanks: 1314  

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