Q . 1 T h e grad i ent f u n ct i on of a cu rve y = ƒ( x) is gi ven by ƒ ( x) = 4x − 5. T h e cu rve p asses t h rou gh t h e p oi n t ( 2, 3) . F i n d t h e eq u ati on of t h e cu rve. Q .2 T h e grap h h as a h or i zon t al p oi n t of i n fl exion at A , a poi n t of i n fl exi on a t B an d a maxi m u m t u r nin g poi n t at C . S k et ch t h e g rap h of f ‘ ( x) Q .3 T h e d i ag ram show s a w i n dow co n sist i n g of t w o sec t ions. T h e t op sectionis a semi ci rcl e of d i amet er x m. T h e b ottom section i s a rec t an gl e of w i d t h ‘x’ m et res an d h ei gh t ‘ y’ m etres. T h e en tire f rame of t h e w i n d ow , i n cl u d i n g t h e pi ece t h at s ep arates t h e t w o sect i ons, i s mad e u si n g 1 0 m of t h i n m et al. T h e sem i ci rc u l ar sec t ioni s m ad e of col ou red gl ass an d t h e rect an gu l ar sect i on i s m a d e of cl ea r gl ass. U n d er test con d i t ions t h e a m ou n t of l i gh t c om i n g t hro u gh on es qu aremet re of t h e col ou red g l ass i s 1 u n i t a n d t h e amou n t of l i gh t comi n g t h rou gh ones qu ar emet r e of t h e cl ea r gl ass i s 3 u n i t s. T h e t ot al amou n t of l i gh t c om i n g t h r ou gh t h e win dow u n der t est condi t i on s is Lu n i t s. Q . 3 T h e di agram ont h e r i gh t h an d si de show s poi n t s A , B , C an d D on t h e g rap h y = f ( x) . A t w h at poi n t s i s f ’ ( x) > 0 a n d f ” ( x) = 0 a A b B c C d D
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