820
Answer Key
153 . (−∞, 0), (0, ∞) 155 . (−∞, −2), (2, ∞)
157 . 2 points 159 . 5 points 161 . c = 2 3 3 163 . c = 1 2 , 1,
3 2
165 . c =1 167 . Not differentiable 169 . Not differentiable 171 . Yes 173 . The Mean Value Theorem does not apply since the function is discontinuous at x = 1 4 , 3 4 , 5 4 , 7 4 . 175 . Yes 177 . The Mean Value Theorem does not apply; discontinuous at x =0. 179 . Yes 181 . The Mean Value Theorem does not apply; not differentiable at x =0.
183 . b =±2 c 185 . c =± 1 π cos
−1 ⎛ ⎞ ⎠ , c =±0.1533 187 . The Mean Value Theorem does not apply. 189 . 1 2 c +1 − 2 c 3 = 521 2880 ; c = 3.133, 5.867 191 . Yes 193 . It is constant. 195 . It is not a local maximum/minimum because f ′ does not change sign 197 . No 199 . False; for example, y = x . 201 . Increasing for −2< x <−1 and x >2; decreasing for x <−2 and −1< x <2 203 . Decreasing for x <1, increasing for x >1 205 . Decreasing for −2< x <−1 and 1< x <2; increasing for −1< x <1 and x <−2 and x >2 207 . a. Increasing over −2< x <−1, 0< x <1, x >2, decreasing over x <−2, −1< x <0, 1< x <2; b. maxima at x =−1 and x =1, minima at x =−2 and x =0 and x =2 209 . a. Increasing over x >0, decreasing over x <0; b. Minimum at x =0 ⎝ π 2 211 . Concave up on all x , no inflection points 213 . Concave up on all x , no inflection points 215 . Concave up for x <0 and x >1, concave down for 0< x <1, inflection points at x =0 and x =1
217 . Answers will vary 219 . Answers will vary 221 . a. Increasing over − π x = − π 2 223 . a. Concave up for x > 4
x < π
x < − π
x > π
x = π
2 , decreasing over
2 b. Local maximum at
2 ; local minimum at
2 <
2 ,
3 , concave down for x = 4 3 225 . a. Increasing over x <0 and x >4, decreasing over 0< x <4 b. Maximum at x =0, minimumat x =4 c.Concave up for x >2, concave down for x <2 d. Infection point at x =2 227 . a. Increasing over x <0 and x > 60 11 , decreasing over 0< x < 60 11 b. Minimum at x = 60 11 c. Concave down for x < 54 11 , concave up for x > 54 11 d. Inflection point at x = 54 11 229 . a. Increasing over x > − 1 2 , decreasing over x < − 1 2 b. Minimum at x = − 1 2 c. Concave up for all x d. No inflection points x < 4 3 b. Inflection point at
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