Given the function f (x) = MX ^ 3 + NX ^ 2 (m n belongs to the real number m > N and is not equal to 0), the tangent of the image at (2, f (2)) is parallel to the X axis Finding the relation between M and n

Given the function f (x) = MX ^ 3 + NX ^ 2 (m n belongs to the real number m > N and is not equal to 0), the tangent of the image at (2, f (2)) is parallel to the X axis Finding the relation between M and n

First, the derivative of F (x) is obtained
The derivative of F (x) is y '= 3mx ^ 2 + 2nx,
The tangent slope of function image at x = 2 is k = 3M * 2 ^ 2 + 2n * 2
K = 12m + 4N
The tangent from the subject is parallel to the X axis
So k = 12m + 4N = 0
M n belongs to real number m > N and is not equal to 0
So 3M = - n