If f(x)={ax+bifx≤2x2−5x+6if2<x≤3px2+qx+1ifx≥3, is differentiable everywhere, then which of the following is correct?

2a+b=0, 9p+3q+1=0, a=2(2)−5 and 2p(3)+q=1, a=−1, b=2, p=49, q=−53

If f(x)={ax+bifx≤2x2−5x+6if2<x≤3px2+qx+1ifx≥3, is differentiable everywhere, then which of the following is correct?

2a+b=0, 9p+3q+1=0, a=2(2)−5 and 2p(3)+q=1, a=−1, b=2, p=49, q=−53

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If $f (x) = {\begin{matrix} a x + b & i f & x \leq 2 \\ x^{2} - 5 x + 6 & i f & 2 < x \leq 3 \\ p x^{2} + q x + 1 & i f & x \geq 3 \end{matrix},$ is differentiable everywhere, then which of the following is correct?

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$a = - 1, q = \frac{5}{3}$

$a = 1, p = \frac{- 4}{9}$

$b = 2, q = \frac{- 5}{3}$

$a = 1, b = 2$

answer is B.

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$2 a + b = 0, 9 p + 3 q + 1 = 0, a = 2 (2) - 5$ and $2 p (3) + q = 1, a = - 1, b = 2, p = \frac{4}{9}, q = \frac{- 5}{3}$

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If f(x)={ax+bifx≤2x2−5x+6if2<x≤3px2+qx+1ifx≥3, is differentiable everywhere, then which of the following is correct?

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If $f (x) = {\begin{matrix} a x + b & i f & x \leq 2 \\ x^{2} - 5 x + 6 & i f & 2 < x \leq 3 \\ p x^{2} + q x + 1 & i f & x \geq 3 \end{matrix},$ is differentiable everywhere, then which of the following is correct?