CHAPTER 4
Analysis of Functions and their Graphs and Other Applications of the Derivative SECTION 4.1 4.1.1 f (x) = x4 − 24x2 (a) Find the largest intervals where f is increasing and where f is decreasing. (b) Find the largest intervals where f is concave up and where f is concave down. (c) Find the location of any inflection points. 4.1.2 f (x) = x4 − 4x3 (a) Find the largest intervals where f is increasing and where f is decreasing. (b) Find the largest intervals where f is concave up and where f is concave down. (c) Find the location of any inflection points. 4.1.3 f (x) = x4 + 8x3 + 24 (a) Find the largest intervals where f is increasing and where f is decreasing. (b) Find the largest intervals where f is concave up and where f is concave down. (c) Find the location of any inflection points. 4.1.4 f (x) = 5x4 − x5 (a) Find the largest intervals where f is increasing and where f is decreasing. (b) Find the largest intervals where f is concave up and where f is concave down. (c) Find the location of any inflection points. 4.1.5 f (x) = 4x3 − 15x2 − 18x + 10 (a) Find the largest intervals where f is increasing and where f is decreasing. (b) Find the largest intervals where f is concave up and where f is concave down. (c) Find the location of any inflection points. 4.1.6 f (x) = x(x − 6)2 (a) Find the largest intervals where f is increasing and where f is decreasing. (b) Find the largest intervals where f is concave up and where f is concave down. (c) Find the location of any inflection points. 4.1.7 f (x) = x3 − 5x2 + 3x + 1 (a) Find the largest intervals where f is increasing and where f is decreasing. (b) Find the largest intervals where f is concave up and where f is concave down. (c) Find the location of any inflection points.
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