Activity A: A. For each of the following functions, find the indicated derivative using the definition. 1. f(x) = 5x + 12; f'(2) 2. f (x) = x2 - 4x + 1; f'(2) 3. f ( x ) = *;f'(-3)Please use this formula: Alternative Definition of the Derivative Let f be a function defined on an open interval / C R, and let x, El. The derivative of the function f at x1 is f'(x) = lim f (x + h) -f(x) h-0 if this limit exists. (This definition of derivative may be used if we are tasked only to find the derivative of the function) Example 10: Let f(x) = 2x2 + 3x - 1. Use the definition of derivative to find f'(-1) Solution: f'(x) = lim (x+h)-f(x) h - = lim [2(+h)2+3(x+h)-1]-(2x2+3x-1) (Substituted ( x + Ax) to all variable) h = lim 2(x2+2xh+h2)+3x+3h-1-2x2-3x+1) h (Expanded expressions) h-0 = lim 2x2+4xh+2h2+3x+3h-1-2x2-3x+1 h-o (Distributive Property of Multiplication) = lim 2x2+4xh+2h2+3x+3h-1-2x2-3x+1) (Combined like terms) h+0 h Page 14 = Jim 4xh+2h-+3h h-0 = lim h(4x+2h+3) (Factored out common monomial) = lim 4x + 2h + 3 h+0 (Simplified form) = 4x + 2(0) + 3 (Evaluated the limit) f' (x) = 4x + 3 To evaluate the function at f'(-1), substitute -1 to the obtained derivative, f'(-1) = 4x + 3 = 4(-1) + 3 =-1