The graph of the function y=x^3 + 6x^2 -2cosx

Question

changes concavity at x =? 

choices are 
a) -1.58 
b) -1.89 
c) -2.33 
d) -1.63 
e) -1.67

 

Answer 1

The function y = x³ + 6x²  - 2 cosx

Apply derivative on each side with respect of x.

y' = 3x²  + 12x + 2 sinx

Again derivative on each side with respect of x.

y'' = 6x + 12 + 2 cosx

Equate the y'' = 0

6x + 12 + 2 cosx = 0

Determine the solution of 6x + 12 + 2 cosx = 0 by graphing.

Observe the graph, the function crosses the x axis at (-1.89, 0).

The function changes concavity at x = - 1.89.

Option b is correct .