Thinking (10 marks) 6. lff(4) = 3 and f'(4) = 5, find g'(4) where 90:) = x/Ex). (3 marks) 7. Given f(x) = ax2 + bx + c , determine the values of a , b , and c if: f'(x) = 6x + 3 and f(2) = 1. (3 marks) 8. Determine the equation of the tangent line to the curve y = x2 3x + 4 at x = 2. (4 marks) 2 DATE 7/ Given data, [(J = ax2+ bx + c f ( 2 ) = - 1 Let differential fly with respect to ; = 8 d x2 + b d 2 + d ( c ) = a ( 2 x ) + b ( 1 ) to plead ) = 2 20 + b Sing , given 2 Compan (1) and 2) , 2ax = 61 a - 3 2 also , b = 3 pyl a = 3 and b = 3 in f (a ) F ( x ) = 3 x 2 + 3x + C Now given, f ( 2) = - 1 f ( 2 ) = 3 ( 2 ) 2 + 3 ( 2 ) + C - 1 = 3 ( 4 ) + 6 + C - 1 = 12+6 + CRefering to page No. 2 We got equation f' () = 2 ax + b 2 Given dalla , Sina, these both flies are equal , we will company coefficient to the right also same ie + b same - + 3 Here, sina left side is same is fl () = mira, then right side aldo equal. and b=3 V 281 = 6 2 - 3