Set, Relation and FunctionEasy
Question
A function y = f(x) has a second order derivative f″(x) = 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)3
D.(x + 1)2
Solution
f″(x) = 6(x - 1) ⇒ f′(x) = 3(x - 1)2 + c
and f′(2) = 3 ⇒ c = 0
⇒ f(x) = (x - 1)3 + k and f(2) = 1 ⇒ k = 0
⇒ f(x) = (x - 1)3.
and f′(2) = 3 ⇒ c = 0
⇒ f(x) = (x - 1)3 + k and f(2) = 1 ⇒ k = 0
⇒ f(x) = (x - 1)3.
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