BASIC CALCULUS (Quarter III, Long Test #3) HPS: 50 points A. CHAIN RULE. Find the derivatives of the following functions. Each item is worth 2 points. HPS: 20 points 1. f(x) = (2x2 - 3x + 1)10 6. f(x) = sec(3x2 -x) 2. f(x) = V4x - 5 7. f (x) = eer 3. f (x) = V1 + VI+x 8. f (x) = i 4. f(x) = x cos 2x 9. f(x) = vsin 3x 5. f(x) = esin3x 10. f(x) = vsin e2x B. IMPLICIT DIFFERENTIATION. Find - by implicit differentiation. Each item is worth 2 points. HPS: 20 points 1. 16x2 + 4y2 = 64 6. yet - xey = In(x + y) 2. ~+4 =1 7. x secy = x -y 3. y2 - 4xy + 2x2 = 10 8. (-3) (x+1) =1 4. ye* + xey = 12 9. ex = cos y 5. 242 = 1 10. V3x + V4y = 5 C. PROBLEM SOLVING. Solve the following problems. Each item is worth 5 points. The scoring guide below will be used to score your responses. ACCURACY OF GRAPH/ The The The The ILLUSTRATION illustration/graph is illustration/graph is illustration/graph is learner correct and the correct but some of Incorrect does not 1.5 points Important the Important try at all Information are Information are not properly labeled properly labeled 1.5 10 0.5 ADEQUATENESS and The learner's The learner's The learner tries to The ACCURACY OF solution is adequate solution is quite solve the problem learner SOLUTION and completely sufficient and/or but his/her solution does not accurate. some of its parts are is not sufficient try at all 3 points Irrelevant or and/or not accurate. Inaccurate. ACCURACY OF The learner will earn the score of 0.5 if and only if he/she gets a correct answer ANSWER and writes it In sentence form. 0.5 point 1. A circle is drawn with its center at (8,0) and with radius r such that the circle cuts the ellipse x2 + 4y = 16 at right angles. Find the radius of the circle. 2. The vertex of the parabola y? = 8x is the center of an ellipse. The focus of the parabola is an end of the minor axis of the ellipse, and the parabola and the ellipse intersect at right angles. Find the equation of the ellipse. BONUS (plus 2 or nothing). If f(x) = x* and g(x) = x3, then f'(x) = 4x] and g'(x) = 3x2. The Chain Rule multiplies derivatives to get 12x5, But f(g(x)) = (x3)* = x12 and its derivative is NOT 12x5. Where is the flaw