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A cubic f(x) = ax 3 + b x 2 +cx + d vanishes at x=2and has relative maximum/minimum at x=1/3 and x= -1. If ∫f(x)dx = 14/3, then what is the value of a+b+c+d?

A cubic f(x) = ax3 + bx2 +cx + d vanishes at x=2and has relative maximum/minimum at x=1/3 and x= -1. If ∫f(x)dx = 14/3, then what is the value of a+b+c+d?

Grade:12

1 Answers

saiomkar kandukuri
33 Points
8 years ago

given f(x) vanishes at x=2

so f(2)=0

so 8a+4b+2c+d=0........(1)

max or min at a point gives differentiation at that pt as zero

diff of f(x) is3ax^2 +2bx +c.....(2)

value of (2)  at x=1/3 ...and at x=-1 is zero

so substitute and get two more equations....

integral of f(x) is (ax^4)/4 +bX^3/3 +cx^2 /2 +dx +e =14/3

now u got equations interms of a,b,c,d find the values and get the answer

 

actually question is not given completely as at which limits integral of f(x) is 14/3 is not given

 

chet it once again and send the question pls

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