Question

The function$f\left(x\right)={\int }_{-1}^{x}t(e^t-1)(t-1)(t-2{)}^3(t-3{)}^{5}dt$ has a local maximum at $x=$

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

f(x)=∫x−1t(et−1)(t−1)(t−2)3(t−5)5dtf(x)=∫x−1t(et−1)(t−1)(t−2)3(t−5)5dt

Using sign scheme rule,

This shows that f(x) has a local maximum at x=0 and x=2