GATE 2018 EE – Question 53

Engineering Mathematics · Calculus: Maxima and minima · 2 marks · Numerical answer

Let $f(x)=3x^3-7x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to 1 decimal place).

Show answer and explanation

Correct answer: 12

Explanation

$f'(x)=9x^2-14x+5=0$ gives $x=1$ and $x=\frac59$. The values are $f(0)=6$, $f(5/9)=7.13$, $f(1)=7$ and $f(2)=24-28+10+6=12$. The maximum is $12$.