Concept explainers
33-44
(a) Find the intervals of increase or decrease.
(b) Find the
(c) Find the intervals of concavity and the inflection points.
(d) Use the information from parts
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Chapter 3 Solutions
Calculus (MindTap Course List)
- Photography A photographer takes a picture of a three-foot-tall painting hanging in an art gallery. The camera lens is 1 foot below the lower edge of the painting (see figure). The angle subtended by the camera lens x feet from the painting is given by =arctan3xx2+4,x0. (a) Use a graphing utility to graph as a function of x. (b) Use the graph to approximate the distance from the picture when is maximum. (c) Identify the asymptote of the graph and interpret its meaning in the context of the problem.arrow_forwardFind the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x, y) = y2 − 10y cos(x), −1 ≤ x ≤ 7arrow_forwarda. The function y = tan x + 3 cot x has an absolute minimum value on the interval 0 < x <pai /2. Find it. b. Graph the function and compare what you see with your answer in part (a).arrow_forward
- 4. Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing graphs (with a graphing device) that display the major features of the curve. Use these graphs to estimate the maximum and minimum values. (Round your answers to three decimal places.) f(x)=((2x+3)^2(x-2)^5)/(x^3(x-5)^2) 4a)find the two local minima pointsarrow_forward(a) Graph f(x) = 2x and g(x) = 12 on the same Cartesian plane.(b) Shade the region bounded by the y-axis, f(x) = 2x , and g(x) = 12 on the graph drawn in part (a).(c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a).arrow_forwardGraph of y = sin 1/x . The discontinuity at x = 0 is not a jump, removable, or infinite discontinuity.arrow_forward
- Find the global maximum and global minimum values of the function g(θ)=2θ−8sin(θ)g(θ)=2θ-8sin(θ) on the interval [0,π][0,π]. Use the derivatives to algebraically answer the question and leave answer in 4 decimal places:The global minimum value = The global maximum value =arrow_forwardFind the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x, y) = 5 sin(x) sin(y), −π < x < π, −π < y < πarrow_forward(a) Find the intervals of increase or decrease.(b) Find the local maximum and minimum values.(c) Find the intervals of concavity and the inflection points.(d) Use the information from parts (a)–(c) to sketch the graph.Check your work with a graphing device if you have one. S (x ) =x - sin x 0≤ x ≤4πarrow_forward
- Find the local maximum and minimum values and saddle point(s) of thefunction. If you have three-dimensional graphing software, graph the function with a domain and view point that reveal all the important aspects of the function.f(x,y) = y2 -2y cos x, -1 ≤ x ≤ 7arrow_forwardThe function y = f(x) = (−1/x) + (1/x^2) on the domain 0 < x < ∞ Find the local maximum and minimum point (x and y coordinates) of the graph. B) Inflection point (both x and y coordinates). C) horizontal and vertical, asymptote of the graph?arrow_forwardFind the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x, y) = y2 − 6y cos(x), −1 ≤ x ≤ 7 local maximum value(s) local minimum value(s) saddle point(s) (x, y, f) =arrow_forward
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