(a) Find the derivative of the function f(x) = m2 + 4 - a: | 7 ..... Derivative of f(x): f'(:c) = (b) When x = 2 then the slope of the tangent line is (c) Write the EQUATION of the line tangent to the graph of f(x) when x = 2 ..... The equation of the tangent line is y = \fLet 1 an) = m _ 1 Use the limit definition of the derivative to find W) = (ii)f'( 1) = w = To avoid calculating four separate limits, I suggest that you evaluate the derivative at the point when m = a. Once you have the derivative, you can just plug in those four values for "a" to get the answers. 6 . Calculate the difference quotient m _ ) f(1 + h) m) f or If someone now told you that the derivative (slope of the tangent line to the graph) of f(m) at :1: = 1 was 1 2 for some integer 71 what would you expect in to be? 11 n = Let f(a:) = 1/3: + 2. Calculate the difference quotient f(34 + h) f(34) f for 112.04% h=.1 1 If someone now told you that the derivative (slope of the tangent line to the graph) of f(:c) at a: = 34 was E for some integer 11 what would you expect 11 to be? 71,: The limit below represents the derivative of some function f(a2) at some number a. 2(1 + h)4 2 lim h>0 h State the function and the number: f =: a: If f(ac) = - 3x2 + 7 + 6, find the instantaneous rate of change of f(a) at x = - 1. Answer =