st K Find the derivative of y = cos X I - with respect to x. The derivative of y = cos * 1 - with respect to x is K Based on data from models the distance the car travels during the time the driver perceives a need to stop until the brakes are applied, and the quadratic term 0.075v ds are applied. Find -at v = 55 and v = 85 mph, and interpret the meaning of the derivative. +Based on data from a research group, a model for the total stopping distance of a moving car in terms of its speed is s = 1.3V + 0.075v2, where s is measured in ft and v in mph. The linear term 1,3v models the distance the car travels during the time the driver perceives a need to stop until the brakes are applied, and the quadratic term 0.075v2 models the additional braking distance once they ds are applied, Find a at v = 55 and v = 85 mph, and interpret the meaning of the derivative. At 55 hds- V- mp'dv Al 85 h dS_ V V- mp'dv , Interpret the derivative. Choose the correct answer below. 0 A. The derivative represents the total time needed for the car to completely stop. 0 B. The derivative represents the distance traveled by the car in feet for a velocity in mph. O C. The derivative represents the additional number of feet needed to stop a car for a 1 mph increase in the speed. O D. The derivative represents the deceleration of the car after the driver applies the brakes. st K A body moves on a coordinate line such that it has a position s = f(t) = 4 2 2 t on the interval 1 Sts 2, with s in meters and t in seconds. a. Find the body's displacement and average velocity for the given time interval. b. Find the body's speed and acceleration at the endpoints of the interval. c. When, if ever, during the interval does the body change direction? The body's displacement for the given time interval is m. (Type an integer or a simplified fraction.) The body's average velocity for the given time interval is m/s. (Type an integer or a simplified fraction.) The body's speeds at the left and right endpoints of the interval are m/s and m/s, respectively. (Type integers or simplified fractions.) The body's accelerations at the left and right endpoints of the interval are m/s and m/s2, respectively. (Type integers or simplified fractions.) When, if ever, during the interval does the body change direction? Select the correct choice below and fill in any answer boxes within your choice. O A. The body changes direction at t= s. (Type an integer or a simplified fraction.) O B. The body does not change direction during the interval. ds are applied. Find at v = 55 and v = 85 mph, and interpret the meaning of the derivative. +K Compute the right-hand and left-hand derivatives as limits and check whether the function is differentiable at the point P. What is the right-hand derivative of the given function? Compose 31 lim f(3 + h) - f(3) 10 h h - 0 y = f(x) Inbox (Type an integer or a simplified fraction.) Starred What is the left-hand derivative of the given function? y = ( x -3)2 - 4 . . Snoozed = 3x - 13 lim f(3 + h ) - f(3 ) h =0 10 h -+ 0 Sent (Type an integer or a simplified fraction.) P(3, - 4) Drafts Is the given function differentiable at the point P? V More 10 O Yes No Labels > Notes Time Remaining: 01:45:03 Next +K Differentiate the function. Then find an equation of the tangent line at the indicated point on the graph of the function. y=f(x) = 3+18-x, (x,y)= (7,4) The derivative of the function y = f(x) = 3 + 18 -x is. What is the equation of the tangent line at (7,4)? O A. y - 4 = - 7 ( X - 7 ) O B. y-4= -2(x-7) O C. y-4=2(x- 7) OD. 2 ( X - 7) +K What is the rate of change of the volume of a ball V= 2 7r 3 with respect to the radius when the radius is r = 2? The volume changes at a rate of]. (Type an exact answer, using it as needed.) are applied. Find - Q +K Find the slope of the graph of the function g(x) = - 7x * + 4 at (3,3). Then find an equation for the line tangent to the graph at that point. 31 7x The slope of the graph of the function g(x) = x + 4 at (3,3) is (Type an integer or a simplified fraction.) 7x The equation for the line tangent to g(x) = - "x+ 4 at (3,3) is y =. Time Remaining: 01:44:44 Next - +K A child flies a kite at a height of 90 ft, the wind carrying the kite horizontally away from the child at a rate of 30 ft/sec. How fast must the child let out the string when the kite is 150 ft away from the child? The child must let out the string at a rate of |ft/sec when the kite is 150 ft away from the child. (Simplify your answer.) models the distance the car travels during the time the driver perceives a need to stop ds are applied. Find - at v= 55 and v = 85 mph, and interpret the meaning of the derivative. +