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find-the-values-of-a-and-b-such-that-the-following-function-differentiable-at-x-1-f-x-x-2-x-1-2ax-b-x-gt-1-




Question Number 90383 by jagoll last updated on 23/Apr/20
find the values of a and b   such that the following  function differentiable at   x=1 f(x) =  { ((x^2 , x≤1)),((2ax+b , x>1)) :}
findthevaluesofaandbsuchthatthefollowingfunctiondifferentiableatx=1f(x)={x2,x12ax+b,x>1
Commented by john santu last updated on 23/Apr/20
(1) lim_(x→1^− )  f(x) = lim_(x→1^+ )  f(x)  ⇒ lim_(x→1^− )  (x^2 ) = lim_(x→1^+ )  (2ax+b)  ⇒ 1 = 2a+b   (2) f ′_1^−  (1) = f ′_1^+   (1)  ⇒2(1) = 2a ⇒ a = 1 ∧ b = −1
(1)limx1f(x)=limx1+f(x)limx1(x2)=limx1+(2ax+b)1=2a+b(2)f1(1)=f1+(1)2(1)=2aa=1b=1

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