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If the derivative of the function \( f(x) \) is everywhere continuous and is given by \( f(x)=\left\{\begin{array}{c}b x^{2}+a x+4 ; x \geq-1 \\ a x^{2}+b ; x |
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Answer» b(1)2 + a(-1) + 4 = a(-1)2 + b b - a + 4 = +a+b ⇒ 2a = 4 ⇒ a = 2 Derivative is continuous 2b(-1) + a = 2a (-1) −2b+a = −2a +2b = +3a b = 3 a/2 b = 3x2/2 ⇒ b = 3 |
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