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1. h(x) is a function with a domain of all real numbers and h'(x) = _6 + 5x (7 - 3x)1/3 a) Find both types of critical points Where slope =0 and Where slope is undefined b) Use the first derivative test to classify the critical points (max, min or neither) Show evidence you used the first derivative test. 2. g(x) is a function with a domain of all real numbers and g'(x) = (cos x)( 2sin (*2x) - 1) a) Find any positive critical points in the interval [0, 1] b) Find the 2" derivative and use it to classify the critical points as max, min or neither. 3. f(t) = (4e%2t) (5x2-2) a) Find f'(t) and determine all critical points. Use a graphing calculator or quadratic formula to determine anything that doesn't factor. Round the decimals to two decimal places. b) Use the first or second derivative test to classify it as maximum, minimum or other. Show clear evidence of which derivative test you used. 4. Find the global max and min for the function f(x) = In (5 + x3) over the interval [-1, 3]. Write CP's in exact form. Show evidence. 5. Given the graph of g '(t), determine the following: Assume g(t) is continuous. g'(t) a) All critical points of g(t) from [-4,4] b) Classify each CP as a local max, min, or neither. c) Allinflection points of g(t) on [-4,4]