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Derivatives-4

Question 1

A street light is at the top of a 13.5 ft. tall pole. A man 6.5 ft tall walks away from the pole with a speed of 5.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 43 feet from the pole? Your answer: ft/secCalculate (f )'(b), where f(x) = x + cos(x ) where b = 1. ( f-1)' (b)Enter INF for oo, -INF for -oo, or DNE if the limit does not exist, but is neither oo nor -oo. lim 3xe lim 3xe = Hence the line y = is a horizontal asymptote to the curve y = 3xe - atConsider the function at) 2 se'm, U s": .1: -00 lim 7xel = Hence the line y = is a horizontal asymptote to the curve y = 7xe atA spotlight on the ground is shining on a wall 16m away. If a woman 2m tall walks from the spotlight toward the building at a speed of 1.2m/s, how fast is the length of her shadow on the building decreasing when she is 41321 from the building? Answer [in meters per second): The length of a rectangle is increasing at a rate of 8011/5 and its width is increasing at a rate of 5cm/s. When the length is 20cm and the width is 15cm, how fast is the area of the rectangle increasing? Answer (in cm2/s): For each of the given functions f(), find the derivative (f-1) (c) at the given point c, first finding a = f-(c). a) f(x) = 4x + 8x3; c= -12 ( f-1 ) ' ( c ) = b) f(ze) = a2 - 15x + 78 on the interval [7.5, co); c = 24 Q= ( f-1 ) ' ( c ) =A street light is at the top of a 12.5 ft. tall pole. A man 5.3 ft tall walks away from the pole with a speed of 3.0 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 49 feet from the pole? Your answer: ft/secFind a and b so that the function f(z) = 823 - 7x2 +7, *