The GATE Grind

GATE 2014 EC (EC2) – Question 13

Engineering Mathematics · Calculus · 1 mark · Multiple choice

For $0\le t<\infty$, where does $f(t)=e^{-t}-2e^{-2t}$ attain its maximum?

  1. $t=\ln4$
  2. $t=\ln2$
  3. $t=0$
  4. $t=\ln8$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $t=\ln4$

Explanation

Differentiate:f′=−e⁻ᵗ+4e⁻²ᵗ. Setting this to zero gives eᵗ=4, so t=ln4. The derivative is positive before this point and negative afterwards; equivalently the second derivative there is negative. Hence the maximum occurs at **t=ln4,A**.