Question
Mathematics Question on limits and derivatives
Let f(x) = x3e–3x, x ^gt 0. Then the maximum value of f(x) is
A
(A) e–3
B
(B) 3e–3
C
(C) 27e–9
D
(D) ∞
Answer
(A) e–3
Explanation
Solution
Explanation:
f(x)=x3⋅e−3x=f′(x)=3x2e−3x+x3e−3x(−3)=x23e−3x[1−x]=0,x=1Maximum at x=1f(1)=e−3