Consider function f(x)=⎧⎪⎨⎪⎩ax(x−1)+b,x<1x−1,1≤x≤3.px2+qx+2,x>3 If f(x) satisfies the following conditionsa)f(x) is continuous for all x.b)f′(1) does not exist.c)f′(x) is continuous at x=3. Then the value of p+q3+1 is

Consider function f(x)=⎧⎪⎨⎪⎩ax(x−1)+b,x<1x−1,1≤x≤3.p

1.	Consider function f(x)=⎧⎪⎨⎪⎩ax(x−1)+b,x<1x−1,1≤x≤3.px2+qx+2,x>3 If f(x) satisfies the following conditionsa)f(x) is continuous for all x.b)f′(1) does not exist.c)f′(x) is continuous at x=3. Then the value of p+q3+1 is
Answer» Consider function $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} a x (x - 1) + b, & x < 1 x - 1, & 1 \leq x \leq 3 . p x^{2} + q x + 2, & x > 3 \end{matrix}$ If $f (x)$ satisfies the following conditions $a) f (x)$ is continuous for all $x$ . $b) f^{'} (1)$ does not exist. $c) f^{'} (x)$ is continuous at $x = 3$ . Then the value of $p + \frac{q}{3} + 1$ is