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function f(x) =x when x ≤1 and ax^2+bx+c when x >1 is differentiable for which set of triplet(a,b,c)

function f(x) =x when x ≤1 and ax^2+bx+c when x >1 is differentiable for which set of triplet(a,b,c)

Grade:11

1 Answers

Kumar
37 Points
4 years ago
Dear friends, If function is differentiable then it must be continuous 
 i.e. function is continuous at x=1 then a+b+c=1 ….... (1)
Function is differentiable at x=1 then 2a+b=1  ….........(2)
And also we say that this function differentiable at x=0 then b=0 …..(3)
Solving the equations (1),(2) and (3), we can get the value of tiplet(a, b, c) is (1/2, 0, 1/2).

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