MATH-1325-PHW_08, 2022-10-15 02:01 3 1. (10 points) For the given function answer the following questions: f (ac) = 2 + 1024- 5x + 3 (a) Find all cut points of the second derivative, f"(x): (b) Give the sign chart of f"(x): (c) Give the corresponding concavity chart of f(a): (d) Give the interval(s) where the function f(x) is concave upward: (e) Give the interval(s) where the function f(x) is concave downward: (f) Give the inflection point (s) in the format (x, y):MATH-1325-PHW_08, 2022-10-15 02:01 2. (10 points) For the given function answer the following questions: f (x) = In(x2 + 16) (a) Find all cut points of the second derivative, f"(x): (b) Give the sign chart of f"(x): (c) Give the corresponding concavity chart of f(a): (d) Give the interval(s) where the function f(x) is concave upward: (e) Give the interval(s) where the function f(x) is concave downward: (f) Give the inflection point (s) in the format (x, y):MATH-1325-PHW_08, 2022-10-15 02:01 5 3. (10 points) Using the Second Derivative Test to find the relative minima/maxima. f (2) = 24 - 823 + 1622 +5 (a) Find the cut points of the derivative, f'(x): (b) Find the second derivative, f"(x): (c) Use the second derivative test to find which cut points of f'(x) correspond to relative maxima, and which correspond to relative minima of f (x): (d) Give the local maximum point(s), in the format (x, y): or NONE (e) Give the local minimum point(s), in the format (x, y): -, or NONEMATH-1325-PHW_08, 2022-10-15 02:01 6 4. (10 points) Using the Second Derivative Test to find the relative minima/maxima. f (ac) = 203-3x2 (a) Find the cut points of the derivative, f'(x): (b) Find the second derivative, f"(x): (c) Use the second derivative test to find which cut points of f'(x) correspond to relative maxima, and which correspond to relative minima of f (x): (d) Give the local maximum point(s), in the format (x, y): or NONE (e) Give the local minimum point(s), in the format (x, y): -, or NONEMATH-1325-PHW_08, 2022-10-15 02:01 7 5. (10 points) Find the global minima/maxima (also known as absolute minima/maxima) of the following function. You must use calculus for any credits.) f (2) = 24 + 423 - 20x2 + 3, where a is restricted to the interval [-1, 3]. (a) Global maximum in the format (x, y): (b) Global minimum in the format (x, y):MATH-1325-PHW_08, 2022-10-15 02:01 8 6. (10 points) Find the global minima/maxima (also known as absolute minima/maxima) of the following function. You must use calculus for any credits.) f(a) = ex-272, where x is restricted to the interval [0, 4]. (a) Global maximum in the format (x, y): (b) Global minimum in the format (x, y):MATH-1325-PHW_08, 2022-10-15 02:01 9 7. (10 points) Find the global minima/maxima (also known as absolute minima/maxima) of the following function. You must use calculus for any credits.) f (a) = In (x2 + 5), where a is restricted to the interval [-1, 3]. (a) Global maximum in the format (x, y): (b) Global minimum in the format (x, y)