Write the first derivative of the given function. f(x) = x5/2In(x) f'(x) = X In(x) For which x-values does f(x) have horizontal tangents? (Enter your answers as a comma-separated list.) X = 0.eA large sphere of material is placed in a dissolving liquid. (a) When the radius is 1 m, it is observed to be changing at 7 cm/hour. At that instant, what is the rate at which the sphere's volume is being dissolved with respect to time? 280000n cm$/hr X (b) Suppose, instead, that the liquid is known to dissolve the material at a rate of 5 m /hour, at what rate will its radius / change with respect to time when / = 1 meter? when r = 1/2 meter? r = 1 0.3979 m/hr r = 1/2 1.5915 m/hr (c) What happens to the rate of change of the radius in part (b) as r - 0+? r - co? 1 0+ 100 0Suppose that fluid is leaking from an overhead pipe and spreading in the shape of a circle on the ground. If the radius of the circle is increasing at a rate of 0.5 feet per minute, how fast is the area of the circle increasing when the radius is 7 feet? 2.199 ft2/min