Consider the function f(x) = 3% + 2. (a) Simplify the following difference quotient as much as possible f(X+h})I-f(X) = 2 (b) Use your result from (a) and the limit definition of the derivative to calculate f'(x)=1imw = z h>0 h _ (c) Use your answer from part (b) to evaluate f'(36) = Z (d) Find the equation of the tangent line to the curve at the point (36, f(36)). y: z Let r(t) = 31' + g. (a) Simplify the following difference quotient as much as possible r(t + h) r(t) _ h ' i (b) Use your result from (a) and the limit definition of the derivative to calculate , _. r(t+h)r(t)_ Wilel i (c) Use your answer from part (b) to evaluate l"(1) = Z (d) Find the equation of the tangent line to the curve at the point (1, r(1)). y: z Let f be the function in the graph below. Express in interval notation where f is differentiable. ANSWER: 2 Note: If the graph of the function is cut off in the vertical direction, that is because the function escapes to either co or oo or both (depending on your graph). Consider the function f (x) = 4x 1. (a) Simplify the following difference quotient as much as possible f(X+h;-f(x) = i (b) Use your result from (a) and the limit definition of the derivative to calculate f'(x)=1imw= z h>0 h _ (c) Use your answer from part (b) to evaluate the following fem: 2 (d) Use your answer from part (c) to find the equation of the tangent line to the curve at the point (2, f (2)). y= Z Consider the function f(x) = x2 x + 5. (a) Simplify the following difference quotient as much as possible f(x+hp),f(X) = 2 (b) Use your result from (a) and the limit definition of the derivative to calculate _m f(x+h)-f(x) = 2 dx _ h>O h _ (c) Use your answer from part (b) to evaluate the following a = 2 dx x=3 (d) Use your answer from part (c) to find the equation of the tangent line to the curve at the point (3, f (3)). y= Z