1.Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using...

1.Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) f(x) = sin(x) + 5 0 < x < 2π increasing decreasing

2. Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) f(x) = x + 2 cos(x), 0 < x < 2π increasing decreasing

3. Consider the following function. f(x) = x + 1 x2 (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) x = (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing decreasing (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum (x, y) = relative minimum (x, y) =

4. s(t) = t3 − 5t2 + 3t − 290 (a) Find the velocity function v(t) of the particle at any time t ≥ 0. v(t) = (b) Identify the time interval(s) on which the particle is moving in a positive direction. (Enter your answer using interval notation.) (c) Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.) (d) Identify the time(s) at which the particle changes direction. (Enter your answers as a comma-separated list.) t =

5. An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 75 miles from the point and has a speed of 450 miles per hour. The other is 100 miles from the point and has a speed of 600 miles per hour. (a) At what rate is the distance between the planes changing?-------- mph (b) How much time does the controller have to get one of the airplanes on a different flight path? -------h

6. An airplane flies at an altitude of y = 5 miles toward a point directly over an observer (see figure). The speed of the plane is 600 miles per hour. Find the rates (in radians per hour) at which the angle of elevation θ is changing when the angle is θ = 30°, θ = 60°,and θ = 80°. (a) θ = 30° rad/hr (b) θ = 60° rad/hr (c) θ = 80° (Round your answer to two decimal places.) rad/hr

7. The formula for the volume of a cone is given below. Find the rate of change of the volume for each of the radii given below if dr/dt is 8 inches per minute and h = 18r. V = (1/3)πr2h (a) r = 9 in V' = π in3/min (b) r = 30 in V' = π in3/min

Expert Solution

Colby Messinger answered 1 year ago

a. find the open intervals on which the function is increasing and decreasing. b. identify the...

a. find the open intervals on which the function is increasing and decreasing. b. identify the functions local and absolute extreme values, if any, saying where they occur. g(x)=x^4-4x^3+4x^2

f(x) = 7xex (a) Find the intervals on which f is increasing or decreasing. (Enter your...

f(x) = 7xex (a) Find the intervals on which f is increasing or decreasing. (Enter your answers using interval notation.) (b) Find the local maximum and minimum values of f. (If an answer does not exist, enter DNE.) (c) Find the intervals of concavity and the inflection points. (Enter your answers using interval notation.)

Determine the open intervals on which the function is increasing and on which the function is...

Determine the open intervals on which the function is increasing and on which the function is decreasing. Enter ∅ to indicate the interval is empty. f(x)=−4x^3−12x^2+36x

Find the open intervals on which ff is increasing (decreasing). Then determine the x-coordinates of all...

Find the open intervals on which ff is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima) for all equations below. 1- f is increasing on the intervals: 2- f is decreasing on the intervals: 3- The relative maxima of f occur at x= 4- The relative minima of f occur at x= a) f(x)= x^3-9x^2+15x+10 b) f(x)= (x-2)/(x+4) c) f(x)= 4 - (8/x) + (8/x^2)

Determine the intervals on which the function below is increasing or decreasing, concave or convex. Determine...

Determine the intervals on which the function below is increasing or decreasing, concave or convex. Determine also relative maxima and minima, inflections points, symmetry, asymptotes, and intercepts if any. Then sketch the curve. . ? = 3?+3/(3? − 3)^2

y=x2/(7x+4) determine the intervals on which the function is increasing, decreasing, concave up, concave down, relative...

y=x2/(7x+4) determine the intervals on which the function is increasing, decreasing, concave up, concave down, relative maxima and minima, inflection points symmetry vertical and non vertical asymptotes and those intercepts that can be obtained conveniently and sketch the graph

1) Find the intervals on which f is increasing and the intervals on which it is...

1) Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x)= -x^3-6x 2) Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x)= x^4/4+x^3+x^2 3) Locate the critical points of the following function. Then use the Second Derivative Test to determine whether they correspond to local maxima, local minima, or neither. f(x)= -x^3-3x^2

Suppose f ' (x) = x2 - 8x + 15 = (x - 3) (x - 5) (a) Identify the intervals of x-values on which f is increasing and the intervals on which f is decreasing.

Suppose f ' (x) = x2 - 8x + 15 = (x - 3) (x - 5)(a) Identify the intervals of x-values on which f is increasing and the intervals on which f is decreasing.(b) Locate where the local maximum point and the local minimum point occur.(c) Identify the intervals of x-values on which f is concave up and the intervals on which f is concave down.(d) Locate any points of inflection.

For f(x)= cos2x + sinx, find the intervals where the function is increasing, decreasing, relative extrema,...

For f(x)= cos2x + sinx, find the intervals where the function is increasing, decreasing, relative extrema, concavity, and points of inflection on the interval [0,2π)

given the function y=x+cosx on the interval [0,2pi] find the intervals of increasing and decreasing, local...

given the function y=x+cosx on the interval [0,2pi] find the intervals of increasing and decreasing, local or absolute extrema(s), the intervals of concavity and the inflection points. use the information to sketch the graph of y=x+cosx on the interval [0,2pi]

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