What are the critical points of #f(x) = e^x(3x^2 - 2x +5)#?

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Answer 1 · 2015-12-02T19:19:47

That function has no critical points.

The domain of #f# is #(-oo,oo)#.

#f'(x) = e^x(3x^2-2x+5)+e^x(6x-2)#

..# = e^x(3x^2+4x+3)#

#f'(x)# is never undefined and it is never #0#.

To see this, solve #e^x(3x^2+4x+3)=0#

#e^x=0# has no solutions and #3x^2+4x+3 =0# has no real solutions.

Therefore, the function has no critical numbers.