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 = 3 x − 5 , then the fun

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 = 3 x − 5 , then the function is

TestHub · Accepted Answer

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

Mathematics - Application of Derivative Question with Solution | TestHub

Options:

Doubts & Discussion