MATH 1325 - Lab 5 - Section 5.3 - Dave Rice Name_ Show your work (except for reading information from graphs or graphing). If you use a calculator to get values, state that. Each question is worth 15 points (6 points for the correct answer and 9 points for showing the work). Use the Test for Concavity to determine where the given function is concave up and where it is concave down. Also find all inflection points. 1. f(x) =x3 +3x2 - x - 24 Find the Possible Inflection Points and use them to find the endpoints of the Test Intervals. Use this table to help with the Concavity Test: Test Intervals Test Points (x) f" (x) Sign of f" (x) CC Up U / CC Down n Inflection Points CC Up Intervals: CC Down Intervals: Inflection Points:3. f(x) = x4 + 4x3 Find the Critical Numbers and use them to find the endpoints of the Test Intervals. Use this table to help with the First Derivative Test: Increasing Intervals: Decreasing Intervals: Local Minima: Local Maxima: 2. f(x) = x4 - 2x2 +7 Find the Critical Numbers and use them to find the endpoints of the Test Intervals. Use this table to help with the First Derivative Test: Test Intervals Test Points (x) f' (x) Sign of f' (x) Incr 71 / Decry Local Extrema Increasing Intervals: Decreasing Intervals: Local Minima: Local Maxima:Use the Second Derivative Test to find the Relative (Local) Maxima and Minima of f(x). 3. f(x) = x3 - 3x2 + 1 f'(x) = Find the Critical Numbers (CNs): CNs: f" (x) = Plug the CNs into f"(x) and perform the Second Derivative Test: Relavtive (Local) Minima in (x,y) format: Relavtive (Local) Maxima in (x,y) format:4. f(x) = x4 - 32x2 -6 f' (x) = Find the Critical Number (CNs): CNs: f" (x) = Plug the CNs into f"(x) and perform the Second Derivative Test: Relavtive (Local) Minima in (x,y) format: Relavtive (Local) Maxima in (x,y) format:MATH 1325 Lab 4 Section 5.2 Dave Rice Name Show your work (excegt for reading information from graphs or graphing). If you use a calculator to get values, state that. Each question is worth 15 points (6 points for the correct answer and 9 points for showing the work). Use the First Derivative Test to find the Relative (Locali Maxima and Minima of x). 1. f(x)=x3 3x2+ 1 Find the Critical Numbers and use them to find the endpoints of the Test Intervals. Use this table to help with the First Derivative Test: Test Intervals Sign off (At) lncr 7| /_ Decr El increasing intervals: Decreasing Intervals: Local Mini-ma: Local Mnxirntt: 2. f (x) = _x4_x3+ 11 Find the Possible Inflection Points and use them to find the endpoints of the Test Intervals. Use this table to help with the Concavity Test: Test Intervals Test Points (x) f" (x) Sign of f" (x) CC Up U / CC Down n Inflection Points CC Up Intervals: CC Down Intervals: Inflection Points