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KurtzTest2

# KurtzTest2 - Sol LA'CO/l 3 Test 2 141-002 Version 2 SHOW...

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Unformatted text preview: Sol LA'CO/l 3 Test 2 141-002 Version 2 SHOW ALL OF YOUR WORK!!!! !! NO CALCULATORS” La (5 points) State the deﬁnition of a derivative for a function f(x). “mm: 3390 M9 i/\ b. (10 points) Use the deﬁnition of a derivative to find f ’(x) for f (x) = V3): + 5. i WA 1 31% W’Q2x+r , aw? 1 H l/\ W? *W _ [C r l — wag/‘0 3% "I‘M 36 % . \ KIA->0- : ““3"”; ”7“» Mmmm 26377 I a, (5 points) Refer to the graph of5(x) pictured below for the following questions: a. Where is 3discontinuous? X : ’3 b. Where is ' not differentiable? , _ .. . -.<' . 3, (10 points) Refer to the graph of f’(x) pictured below for the following questions: ‘ 3 i a. On what intervals is f(x) increasing? ’ (' 0C! 3 «- I a b\ (e 0 Li ) Z} (7? ‘ S ) 00 b. Where does f have local maximums? )(c v] 4 (a X =a ~ c. On what intervals is f”(x) < 0? [r Ob \" l \ ( l ) 33 d. On what intervals is f(x) concave downwards? W ._ t (’00)‘D CH3 I .2 / q.(lopoimsmndfxx)irf(x)=cot(7x)+—42-+R/§+e'""ﬁ :CC>+‘(7K) + 9x +X &*\H/ X 42%“: ~CSC?(7)<)1’7 ng‘g eggs/é 5. (10 points) ﬁnd f’ (x) if f(x)=2"‘(14:3 +e‘x) new Nanchaw ﬂat 6 ) 6. (10 points) Using the quotient rule ﬁnd f’(x) if f(x) = tanx '2 8 [a 5_< Cos K ' \ . \ ‘ ‘ ‘ ‘ ”G (X) — CO§XCOSK ,.- S] AX (~5I AX) _(Oy7x+smzx=‘i @052 x ‘ cosz x ,L : Cafx 1 S€c2x 7. (15 points) Fund an equation of the tangent line to (x2 + y2)2 = xy2 +y at (0,1). .- .. --_— .._..—o . . dy _ x x s; (10 pomts)F1nd a where y — (secx) “VT 1 [A (SQQXB M91: »( \Asecy .L &%X : \Asecsz + X'Sz/S‘fgi éi : “max + ka> 61. (15 points) Refer to the chart for the following questions. a. If F(x) = f(g(X)), ﬁnd F'(3) Fm: ¥'(j<><>\~j‘(><\ "F‘(%):£((cj(z\\3‘(s) 190%) : 6234 3‘11 b. If H(x) = ﬂ, find H’(2). g(x) ...
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