A function y =f(x) has a second order derivative f"=6(x-1). If its graph passes through the point(2,1) and at that point the tangent to the graph is y =3x -5, then the function is
Options:
A .  
(x−1)2
B .  
(x−1)3
C .  
(x+1)2
D .  
(x+1)3
Answer: Option B : B Since f"(x)=6(x-1) ⇒f′(x)=3(x−1)2+c (integrating) ----(i) Also, at the point (2,1), the tangent to the graph is y =3x-5and slope of thetangent = 3 ⇒f′(2)=3 3(2−1)3+c=3 [from eq(i) ⇒3+c=3⇒c=0 From Eq (i) we have f′(x)=3(x−1)2 ⇒f(x)=(x−1)3+k (Integrating)----(ii) ∴1=(2−1)3+k⇒k=0 Hence the equation of the function is f(x)=(x−1)3.
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