Let f{z) = 7z + 2. Determine the instantaneous rate of change at z = 5. rate of change of f at = b: D \fLet f(z) = vz + 1. Calculate the difference quotientw for each value of h below. h=.1 h=.01 h=-.01 h=-1 If someone told you that the derivative (slope of the tangent line to the graph) of f(m) atz = 24 was 1 for some integer iz what would you expect n to be? o To verify your prediction, make a plot that includes the graph of y = f(a;) near the point (z, y) = (24, 5) along with the graph of the tangent line through that point. Let F(z) be the function whose graph is shown below. 110 1.0 Determine F' (a) for a = 1, 2, 4, 7. F(1) = F' (2) = F'(4) = F' (7) =Let p(x) = 24/=. (a) Find the slope of the function's graph at = 16. Slope = p'(16) = E] (b) Find an equation for the line tangent to the graph of = p(z) at the point (z,y) = (16, 8). Tangent line: y = D To verify your results, make a plot that includes the graph of y = p(:z;) near the point (w, y) = (16, 8) along with the graph of the tangent line through that point. Let w(x) = 2x + 3. Fill in the blanks below. w'(-1) is the limit as a -> of the expression The value of this limit is Fill in the right-hand side of the equation below so it is the equation of a line tangent to the graph of y = w(x) at a = -1. y1 For p(z) = +3, use the limit definition of the derivative to find the derivatives below. To avoid calculating four separate limits, compute the limit with 2 = a. Then, substitute for a to find the derivative at the given points. () p/(0) = (i) p' (1) = (iiiy p'(5) = (iv) p'(6) =