If the function f given by f x = x 3 - 3 a - 2 x 2 + 3 a x + 7 , for some a ∈ R is increasing in 0 ,   1 and decreasing in 1 ,   5 , then a root of the equation, f x - 14 x - 1 2 = 0 ,   x ≠ 1 is :

Question

If the function f given by f x = x 3 - 3 a - 2 x 2 + 3 a x + 7 , for some a &#8712; R is increasing in 0 , &#160; 1 and decreasing in 1 , &#160; 5 , then a root of the equation, f x - 14 x - 1 2 = 0 , &#160; x &#8800; 1 is :

Aicharya · Accepted Answer

At x = 1 , &#160; f &#8242; x = 0 &#8756; &#160; f &#8242; x = 3 x 2 - 6 a - 2 x + 3 a Now, f ' 1 = 0 &#8658; 3 - 6 &#160; a - 2 + 3 a = 0 &#8658; a = 5 &#8756; &#160; f x - 14 x - 1 2 = 0 &#8658; x 3 - 9 x 2 + 15 x - 7 x - 1 2 = 0 &#8658; x - 7 x 2 - 2 x + 1 x - 1 2 = 0 &#8658; x - 7 = 0 &#8658; x = 7

If the function f given by f x = x 3 - 3 a - 2 x 2 + 3 a x + 7 , for some a ∈ R is increasing in 0 ,…

Solution

If the function f given by f x = x 3 - 3 a - 2 x 2 + 3 a x + 7 , for some a &#8712; R is increasing in 0 ,…

Solution

If the function f given by f x = x 3 - 3 a - 2 x 2 + 3 a x + 7 , for some a ∈ R is increasing in 0 ,…