Consider the piecewise function p(x)= cases ax+b,& x<1

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Consider the piecewise function p(x)={ax+b,x<1,ax2,1≤x<4,bx+3,x≥4.p(x)= \begin{cases} ax+b,& x<1,\\ ax^{2},& 1\le x<4,\\ bx+3,& x\ge 4. \end{cases} For which ordered pair (a,b)(a,b) is pp continuous for all real numbers? (a) (0, 0)\left(0,\,0\right) (b) (34, 0)\left(\dfrac{3}{4},\,0\right) (c) (14, 0)\left(\dfrac{1}{4},\,0\right) (d) (316, 0)\left(\dfrac{3}{16},\,0\right)

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