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13 Nov 2019
QUESTION 3
Lab Report 3 Instructions: use the first and second derivatie to complete the following problems. 1. Let y = ax2 + bz + c be a parabola with real coeffecients a, b, and c. (a) Show that the vertex always occurs at x = 20 (b) Show that a parabola is always concave up or concave down and has no inflection points. What determines the concavity of the parabola? 2 Letyar3 + ba2+cr + d be a third degree polynomial with real coefficients. (a) Show that this polynomial has exactly one inflection point. Find the a-coordinate of this inflection point in terms of a, b and c. (b) If the graph of a cubic has three z-intecepts, ki, k2 and 3, show that the r-coordinate of the infeciton point is (kit k2 + k3)/3. 3. In this problem we will prove that e 2+1 for all values of z. (a) Let f(z)1). Using f(x) find the local max or min of this function. Then fill in the blanks of this sentence: At x =ã¼ã¼/(x) has a local--_ of y =- (b) Based on what you found in the previous problem, fill in the blank with the appropriate inequality: For all values of x, f(x)1. Then explain why this statement is true. (c) Use what you wrote in part b) to show that e 2 +1.
QUESTION 3
Lab Report 3 Instructions: use the first and second derivatie to complete the following problems. 1. Let y = ax2 + bz + c be a parabola with real coeffecients a, b, and c. (a) Show that the vertex always occurs at x = 20 (b) Show that a parabola is always concave up or concave down and has no inflection points. What determines the concavity of the parabola? 2 Letyar3 + ba2+cr + d be a third degree polynomial with real coefficients. (a) Show that this polynomial has exactly one inflection point. Find the a-coordinate of this inflection point in terms of a, b and c. (b) If the graph of a cubic has three z-intecepts, ki, k2 and 3, show that the r-coordinate of the infeciton point is (kit k2 + k3)/3. 3. In this problem we will prove that e 2+1 for all values of z. (a) Let f(z)1). Using f(x) find the local max or min of this function. Then fill in the blanks of this sentence: At x =ã¼ã¼/(x) has a local--_ of y =- (b) Based on what you found in the previous problem, fill in the blank with the appropriate inequality: For all values of x, f(x)1. Then explain why this statement is true. (c) Use what you wrote in part b) to show that e 2 +1.
Reid WolffLv2
9 Apr 2019