Let a be a real number such that the function f ( x ) = a x 2 + 6 x - 15 , x ∈ R is increasing in - ∞ , 3 4 and decreasing in 3 4 , ∞ . Then the function g ( x ) = a x 2 - 6 x + 15 , x ∈ R has a

Step-by-step solution

We have, f x = a x 2 + 6 x - 15 Graph of f x is shown below as it is increasing in - ∞ , 3 4 and decreasing in 3 4 , ∞ . Then, abscissa of vertex is 3 4 . - B 2 A = 3 4 ⇒ - ( 6 ) 2 a = 3 4 ⇒ a = - 4 ∴ g ( x ) = - 4 x 2 - 6 x + 15 Local maxima exists at the vertex of g x , whose abscissa is x = - B 2 A ⇒ x = - - 6 - 8 = - 3 4