\fTangent Line. If p(x) = 4x2 + 8x3 + 4 3 + 2 Then the equation of the tangent line to the function p(x) at x = 1 is None of the other answers Oy = 20x Oy = 22x Oy = 22x + -4 Oy = 22x + 16 Oy = 20x + -4 Oy = 20x + 18 Oy = 20x + -2Differentiable Function. If a differentiable function f(x) satisfies f(-1) = f(1) then there exists a c in (-1,1) with Of" ( c ) = 0 Of(c) = 0 Of ( c ) > 0 Of" ( c ) 0 Of ( c ) = 0 Of (c) > 0Suppose a person travels at a rate of 7 ft/hr toward the foot of a street lamp pole 53 ft high. The height of the person is 5.3 ft. At what rate is the distance from the head of the person to the top of the street lamp changing when 76 ft from the bottom of the street lamp? Note: Round your answer to 4 decimal places. O -6 ft/hr O O ft/hr none of the other answers 5.7417 ft/hr 0.1687 ft/hr O -0.1687 ft/hr 5.9290 ft/hr O 5.5541 ft/hrArea. Suppose the area of a circle is decreasing at a rate of2m2/sec, the rate of change of the radius when the area i512m2 equals A 6.1400 m/s A 150.7964 m/s A -6.1400 m/s A -150.7964 m/s A -0.1629 m/s A 0.1629 m/s \fImplicit Differentiation. The demand equation for a certain brand of two-way headphones is 5x3+8xy + 2y2 = 19 where x represents the number (in thousands) of headphones demanded each week when the unit price is y. Find dy by implicit differentiation for the given equation. dx O none of the other answers dy -15x2 O dx +8 + 4y dy 15x-+8y dx +8x + 4y dy -(15x2+8y) O = dx +8x + 4y dy -15x2 dx +8x + 4yDetermine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. In(a) - In(b) = In(a - b) for all positive real numbers a and b. True. Take a = 4 and b = 2. Then In(a) - In(b) = In(4) - In(2) = In 2 = In(2). And In(a - b) = In(4 - 2) = In(2). True. This is one of the Laws of Logarithms. False. In(a - b) = In(a) - In(b) only for negative real numbers a and b. False. In(a - b) = In(a) - In(b) only for positive real numbers a > b. False. Take a = 2 and b = 1. Then In(a) - In(b) = In(2) - In(1) = In(2) - 0 = In(2). But In(a - b) = In(2 - 1) = In(1) = 0.\fInterest Formula. Suppose you work at a bank and the manager provides a new type of formula to calculate interest when merging two loans together. Suppose there are two loans with one interest rate at 3% and a second loan at 4%. The manager writes the first part of the formula for the new interest rate as e(3In(4) + 4ln(3)) which of the following is equivalent to the manager's expression? (j ee4+es1 r) e2592 b 65184 F) 2592 i'\" 0 b 5184 h 6'17 r) 145 miElectrIc CurrentSupposeyouhavetwoelectronlcdeVIcesthathavedlfferentcurrentswhenx . Suppose f(x) is the function that describes the current in both devices and a is an additional tool to change the current of the first device to match the current of the second device. a+3x+4x2 ifx