Calculus I (Math-UA-121) Fall 2016-HW 9 Section 4.2 1. Suppose we know that 3 f 0 (x) 5 for all values of x. What is the smallest and largest value of f (8) f (2)? 2. Show that the equation has exactly one solution: x3 + ex = 0 3. Use the Mean Value Theorem to show that | sin(a) sin(b)| |a b| for all a and b. Section 4.3 4. Find the critical points and inflection points. Determine the local extrema and the intervals where the function is concave upward and concave downward. (a) f (x) = 4xe3x ; (b) f (x) = x sin(x), x [ 2 , 3 2 5. Sketch the graph of a function that satisfies 0 0 f (2) = f (2) = 0; 0 f (x) < 0 for |x| < 2; f 0 (x) > 0 if 2 < x < 4; 00 f (x) < 0 for x (4, 0); 0 f (x) = 0 for x > 4; f has an inflection point at (0, 2) Section 4.4 (Optional, will not grade) 6. Do a full analysis (carrying out steps A-H from the textbook) on the following functions: (a) f (x) = ex + ex (b) f (x) = tan1 x1 x+1 \u0001 1