17. [0/1 Points] DETAILS PREVIOUS ANSWERS TANAPCALC10 5.5.060. Find the inflection point of the function f(x) = x6 In(x). (If an answer does not exist, enter DNE.) (x, y) = DNE Need Help? Read It Watch It TANAPCALC10 5.5.067. 18. [-/1 Points] DETAILS dy Find dx dy dx dy dx dy dx dy dx dy dx by implicit differentiation. = = = = In(x) + xy = 2 = 2 - 3xy 2 + 3xy 2 + 3xy 3 - 2xy 3 + 2xy x3 Need Help? Read It 19. [-1/2 Points] DETAILS TANAPCALC10 5.5.076. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Depreciation of Equipment For assets such as machines, whose market values drop rapidly in the early years of usage, businesses often use the double declining-balance method. In practice, a business firm normally employs the double declining- balance method for depreciating such assets for a certain number of years and then switches over to the linear method. The double declining-balance formula is V(n) = C (1 - 2)" N where C is the initial value of the asset in dollars, V(n) denotes the book value of the assets at the end of n years, and N is the number of years over which the asset is depreciated. A tractor purchased at a cost of $55,000 is to be depreciated by the double declining-balance method over 10 years. (a) What is the book value (in dollars) of the tractor at the end of 2 years? $ (b) What is the relative rate of change of the book value of the tractor at the end of 2 years? 20. [-/2 Points] DETAILS TANAPCALC10 5.5.085. Magnitude of Earthquakes On the Richter scale, the magnitude R of an earthquake is given by the formula R = log where I is the intensity of the earthquake being measured and I is the standard reference intensity. (a) What is the magnitude of an earthquake that has intensity 100 thousand times that of I? MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (b) Suppose an earthquake is measured with a magnitude of 5 on the Richter scale with an error of at most 2%. Use differentials to find the error in the intensity of the earthquake. Hint: Observe that I = 1010 R and use logarithmic differentiation. (Round your answer to two decimal places.) 10 21. [-/1 Points] DETAILS Sketch the curve f(x) TANAPCALC10 5.5.089. =4x-In(x), using the guidelines below. Guidelines for Curve Sketching 1. Determine the domain of f. 2. Find the x- and y-intercepts of f. 3. Determine the behavior of f for large absolute values of x. 4. Find all horizontal and vertical asymptotes of f. 5. Determine the intervals where f is increasing and where f is decreasing. 6. Find the relative extrema of f. 7. Determine the concavity of f. 8. Find the inflection points of f. 9. Plot a few additional points to help further identify the shape of the graph of f and sketch the graph. f(x) f(x) -5 5 -5 Need Help? Read It Watch It x 5 -5 5 -5 x 5 -5 f(x) 5 -5 5 x -5 f(x) -5 5 x MY NO