OO Verizon '3 fl newclasses.nyu.edu 2:28 PM Assignment 4, Math for Economics 1 (28 points) Write neat solutions [or the problems below. Show all your work. if you only write the answer with no work, you will not be given any credit. Please do not lbrget. to: Write your name and recitation section number. Staple your homework if you have multiple pages! 1. (5 pts) Let [(x) = VJ: - 3. Find f'(7) using a limit definition of the derivative. On one graph, sketch f and sketch the line tangent. to f at (7.2). 2. (4 pts) Let. [(x) = I l-u: Find a formula for ['(a) (assuming a afi 1) using a limit delinition ol" the derivative. 3. (4 pts) The derivative ol" some function g(1:) is graphgl below. (a) On what intervals is g increasing? (li) For what z-value(s) is the tangent line for 9 horizontal? 4. (4 pts) A function f(;r) is graphed below. Use it to sketch the graph of f' O '- -mew'Mu0thl-Lnnunnl < 5. (4 pts) Let. [(x) = le. Graph f'(:r). Clearly indicate the domain of f'. 6. (4 pts) Find Il - ' lln -ol) > "327 + II - 3 , h in two steps:OO Verizon 4? 2:28 PM E- n newclassesnyuedu fi Wim-mimi"; (b) For what x-valnc(s) is the tangent. line {or 9 horizontal? 4. (4 pts) A function f(z) is graphcd below. Use it to sketch the graph of f'(:::). O F 5. (4 pts) Let [(1) = '1'. Graph f'(x). Clearly indicate the domain of f'. {WIT-ti -3. 6. (4 pts) Find lin) Ill two steps: h-tfl h 6/27' + IT - 3 (a) (2 pts) Find a function f and a number rr such that f'(a.) = h (b) (2 pts) Evaluate f'(a) using the power rule. (Your answer in (l)) should be a number, not an abstract expresion involving a) 7. (3 pts) By combining the power and addition rules for differentiation. find f'(z) if {(z)=s"/8-x+-3- 1:1/4' Some extra problems (not. to be handed in) 1. Using a limit. definition of the derivative. lind f'(a.) if {(1) = zr: - fi. 2 2. Find the equation of the line tangent. to the graph of [(z) = x "El at (l, 2). 3. Suppose f(1:) = axz + bx + c, where n.b,c are constants and rr ; 0. Show that. ['(x) = 0 if and only if x = - 210. This shows that. at the parabola's vertex, the tangent. line is horizontal. l ifISO HI): 12+l ifr>0 4. (Challenge problem!) Let Is I is dill'erentiable at 0'.' If so. use a limit. definition of the derivative to lind f'(0)