Find the maximum and minimum value of the function f(x)=x2ex.
f(x)=x2ex
ex>0∀ x∈R
also x2>0∀ x∈R
∴ minimum value ocues at x=0
∴ f(0)=(0)Le0=0
∴ minimum value of f(x)=0
f′(x)=2xex+x2ex
f′(x)=2ex+2xex+2xex+x2ex
f(x) is on increasing function.
So, f(x) reads infinity as xaxis.
∴ f(x)∈[0, ∞]