Question

Is f(x)=x2−x increasing or decreasing at x=1?

Answer 1

$\huge\mathbb{HEYA}$


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To know that, you are finding the slope at x=1, and seeing if it is positive or negative (or 0, but in that case it would be an extremum).

dfdx=ddx[x2ex]

=x2ex+2xex (product rule)

=ex(x2+2)

Thus, at x=1:

f(1)=e1((1)2+2)

=3e>0

So, the function is increasing at x=1.

hope it helps you..

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