Let f(x) = {([x] + sgn(x^2), -2 le x < 2),(ax^(2) - bx, x ge 2):} If the number of points where f(x) is nonderivable in [–2, oo) is 3 then the value of |a + b| is (Note: [y] and sgn (y) denote greatest integer function and signum function of y respectively).

Let f(x) = {([x] + sgn(x^2), -2 le x < 2),(ax^(2) - bx, x ge 2):} If

1.	Let f(x) = {([x] + sgn(x^2), -2 le x < 2),(ax^(2) - bx, x ge 2):} If the number of points where f(x) is nonderivable in [–2, oo) is 3 then the value of \|a + b\| is (Note: [y] and sgn (y) denote greatest integer function and signum function of y respectively).
Answer» Solution :`F(X) = {([x] + sgn(x^2), -2 le x < 2),(ax^(2) - bx, x ge 2):}` `{(-1,",", -2 le x < -1),(0,",", -1 le x < 0),(1,",", 0 < x < 1),(2,",", 1 le x < 2),(ax^(2) - bx,",", x ge 2):}` For only 3 points of non-derivable in `[-2, OO)` Then it should be derivable at x = 2 So, `f(x) = 2, [ "At" x = 2]` `f'(2) = 0 [ "At" x = 2]` `4A - 2b = 2 ""......(1)` `4a - b = 0 ""......(2)` From (1) & (2) `a = -1/2 & b = -2` `\| a + b \|= 2.50`

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Let f(x) = {([x] + sgn(x^2), -2 le x < 2),(ax^(2) - bx, x ge 2):} If the number of points where f(x) is nonderivable in [–2, oo) is 3 then the value of |a + b| is (Note: [y] and sgn (y) denote greatest integer function and signum function of y respectively).

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