f (x)= x^2cos(3x). is f increasing or decreasing at x=4 and what concavity is at x=4

Question

Calculas Help

Answer 1

Evaluate f'(x).

 

f'(x) = 2xcos(3x) + x² (-3sin(3x))

 

f'(x) = 2xcos(3x) - 3x²sin(3x)

 

f'(4) = 2(4)cos(12) - 3(4)²sin(12)

 

f'(4) = 8cos(12) - 48sin(12)

 

f'(4) = 32.58

 

It is increasing because derivative is positive.

 

 

Now find f''(x).  Then

 

Evaluate f''(4).

 

If f''(4) is negative, then concave down.

If f''(4) is positive, then concave up.