## Question

###### Is #f(x) =(x+1)^3+3x^2+4x-3# concave or convex at #x=-1#?

Is #f(x) =(x+1)^3+3x^2+4x-3# concave or convex at #x=-1#?

## Answers

The second derivative is positive, hence the curve is concave upwards at

#x=-1# ## Explanation:

Given -

#f(x)=(x+1)^3+3x^2+4x-3#

#f'(x)=3(x+1)^2(1)+6x+4#

#f'(x)=3(x+1)^2+6x+4#

#f''(x) = 6(x+1)+6#

#f''(x)=6x+6+6#

#f''(x)=6x+12# At

#f''(x) = 0; 6x+12=0#

#6x=-12#

#x=-12/6=-2# At

#x=-2# there is point of inflextion.At

#x=-1; f''(x)= 6(-1)+12=6>0# At

#x=-1# The second derivative is positive, hence the curve is concave upwards at#x=-1#

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