Search for: Let f(x) be a function such that,f(0)=f′(0)=0 ,f′′(x)=sec4 x+4 then the function is Let f(x) be a function such that,f(0)=f′(0)=0 ,f′′(x)=sec4 x+4 then the function is Alog |(sin x)|+13tan3 x+xB23log |(sec x)|+16tan2 x+2x2Clog |(cos x)|+16cos2 x+x5DNone of the above 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:Since,f′′(x)=sec4 x+4f′′(x)=1+tan2 xsec2 x+4⇒ f′(x)=tan x+tan3 x3+4x+C⇒f′(0)=0⇒0=C Then, f′(x)=tan x+tan3 x3+4xf′(x)=tan x+tan3 x3+4x=tan x+13tan xsec2x−1+4x⇒ f′(x)=23tan x+13tan xsec2 x+4x∴ f(x)=23log |sec x|+tan2 x6+2x2+d But f(0)=0⇒d=0 Then, f(x)=23log |sec x|+16tan2 x+2x2Post navigationPrevious: If a parallelepiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel tothe coordinate planes, then the length of diagonal of the parallelepiped isNext: If x2+y2=1 then the distance from the point x,y,1−x2−y2 to the origin isRelated 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