Show that f(x) = (x - 1)ex + 1 is an increasing function for all … - Vidyadip

Question

Show that f(x) = (x - 1)e^x + 1 is an increasing function for all x > 0.

✓

Answer

f(x) = (x - 1)e^x + 1

f'(x) = (x - 1)e^x + e^x

= xe^x - e^x + e^x

= xe^x

Given: x > 0

We know,

e^x> 0

⇒ xe^x > 0

⇒ f'(x) > 0, for all x > 0

So, f(x) is increasing on for all x > 0.

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