Search for: The value of c in Roll’s theorem for the function f(x)=x(x+1)ex defined on [−1,0], isThe value of c in Roll's theorem for the function f(x)=x(x+1)ex defined on [−1,0], isA0.5B1+52C1−52D-0.5 Register to Get Free Mock Test and Study Material +91 Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:We have, f(x)=x(x+1)e−x,x∈[−1,0]∴ f′(x)=−x2−x−1e−x,f(−1)=0,f(0)=0Hence, f′(x)=f(0)−f(−1)0−(−1)⇒ −x2−x−1e−x=0⇒x2−x−1=0⇒x=1±52Hence, c=1−52Post navigationPrevious: If f(x)=alog|x|+bx2+x has its extremum values at x=-1 and x=2, thenNext: The equation sinx+xcosx=0 has at least one root in the interval Related content JEE Main 2023 Question Papers with Solutions JEE Main 2024 Syllabus Best Books for JEE Main 2024 JEE Advanced 2024: Exam date, Syllabus, Eligibility Criteria JEE Main 2024: Exam dates, Syllabus, Eligibility Criteria JEE 2024: Exam Date, Syllabus, Eligibility Criteria NCERT Solutions For Class 6 Maths Data Handling Exercise 9.3 JEE Crash Course – JEE Crash Course 2023 NEET Crash Course – NEET Crash Course 2023 JEE Advanced Crash Course – JEE Advanced Crash Course 2023