Chapter 4 | Applications of Derivatives
405
212.
215.
213.
For the following exercises, draw a graph that satisfies the given specifications for the domain x = [−3, 3]. The function does not have to be continuous or differentiable. 216. f ( x ) >0, f ′( x ) >0 over x >1, −3< x <0, f ′( x ) =0 over 0< x <1
f ′( x ) >0 over x >2, −3< x <−1, f ′( x ) <0
217.
over −1< x <2, f ″( x ) <0 for all x
f ″( x ) <0
218.
over
−1< x <1, f ″( x ) >0, −3< x <−1, 1< x <3, local maximum at x =0, local minima at x =±2 219. There is a local maximum at x =2, local minimum at x =1, and the graph is neither concave up nor concave down. 220. There are local maxima at x =±1, the function is concave up for all x , and the function remains positive for all x . For the following exercises, determine a. intervals where f is increasing or decreasing and b. local minima and maxima of f . 221. f ( x ) = sin x +sin 3 x over − π < x < π 222. f ( x ) = x 2 +cos x For the following exercises, determine a. intervals where f is concave up or concave down, and b. the inflection points of f . 223. f ( x ) = x 3 −4 x 2 + x +2
214.
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