At x 2 the function y Ln3x2 2x3 7x 1 is To check if a f

At x = 2, the function y = Ln(3x^2) - 2x^3 + 7x + 1 is: To check if a function is increasing/decreasing and concave up/down, you need to find y\' (positive means increase, negative means decrease) and y\" (positive means concave up, negative means concave down) at the point!! Decreasing, concavity cannot be determined from the information given. Decreasing and concave down. Increasing and concave down Increasing, concavity cannot be determined from the information given. Increasing and concave up Decreasing and concave up

Solution

y = ln(3x^2) -2x^3 + 7x +1

y\' = -6x^2 + 2/x +7

y\'=0 ; -6x^2 + 2/x +7 =0

Plug x= 2 in y\' = -6(2)^2 + 2/2 + 7 = -16

So, y\' is -ve .It means function is deceasing

Concave up/down; find y\"

y\"= -12x - 2/x^2 at x= 2

y\" = -49/2

So, It means concave down

So, Option Decreasing with concave down