Home › Previous year questions › GATE 2019 AE › Question 11GATE 2019 AE – Question 11 Engineering Mathematics · Calculus: Limits, continuity, differentiability, chain rule, maxima and minima, integration · 1 mark · Multiple choice
For real x, what is the maximum value of $f(x)=xe^{-x}$?
$1/e$ $2/e^2$ $e^{-1/2}/2$ $\infty$ Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (A) $1/e$
Explanation Differentiate: $f\prime=e^{-x}(1-x)$. The function increases up to x=1 and decreases afterwards. Its value there is 1/e; as x tends to negative infinity the function tends to negative infinity. Thus the global maximum is 1/e, A.
More Calculus: Limits, continuity, differentiability, chain rule, maxima and minima, integration questions GATE 2019 AE Q24 – For f(x)=12(x+ x ), evaluate -11f(x)\,dx. GATE 2019 AE Q25 – Evaluate 0(-)/3 (two decimal places). GATE 2019 AE Q41 – How many points of intersection do y=x and y=cos x have? GATE 2024 AE Q37 – The volume of the solid formed by a complete rotation of the shaded portion of the circle… GATE 2024 AE Q45 – Consider the function f(x) = cases x2 & for x < 0 \\ x & for x 0 cases where x is real.… GATE 2025 AE Q15 – f(x) = cases A + x, & x < 2 \\ 1 + x2, & x 2 cases If the function f(x) is continuous at x… All Calculus: Limits, continuity, differentiability, chain rule, maxima and minima, integration questions →