RE Quadratic functions 2 a.? Show th ? a?t i?? ,? ? )) is any point on the gr?ap? h of ?f(x? ?) = x , then the slope of the tangent line at that p?oint i?s m ? = 2?a. b.? Sho? ? t?hat if (?a, ?f(?a)) is any point on t? e? graph ? f ?? ?) =? x + c ? x + ? , then the slope of the tangent line at t?hat poi? nt i?s ?m = 2?ab + c ? .

Solution Step 1: Given the graph of ) = x2 we have to show tha t if (a, f )) is any point on the grap h of ) = x , then the slope of the tangent line at that p oint is m = 2 . Recall that the geometrical meaning of derivative at any point is slope of the tangent line at that point Therefore to show the slope of the tangent line we have to find the derivative of f(x)=x at (a, (a)) (a) Given f(x ) = x2 f’(x)= (f(x)) dx d 2 = dx ) d f’(x)=2x ( dx ) = nx n1 ) (a, )) is any po in t on the graph of f ) = x2 The slope of the tangent line at point (a,f(a)) is f(x) = 2x (a,f(a)) (a,f(a) =2a Therefore m=2a the slope of the ta ngent line at that point is m = 2a . Step 2: (b) Given f(x ) = x + c x + d, f’(x)= (f(x)) dx d 2 = dxx +cx+d) d f’(x)=2bx+c (dxx ) = nx n1 ) ( , )) is any point on the graph of f (x) = x + cx + d,