The derivative of a function is f'(x)=-6x^2(x-1)(x+2). How can I identify any local extrema of f,...

The derivative of a function is f'(x)=-6x^2(x-1)(x+2). How can I identify any local extrema of f, if any? How can use the First Derivative test to determine if any of the local extreme identified are a relative maximum or a relative minimum?

Expert Solution

milcah answered 2 years ago

Consider the function f(x)=(2x−1)e^−6x. Determine the critical point(s) of f and locate all local extrema, then...

Consider the function f(x)=(2x−1)e^−6x. Determine the critical point(s) of f and locate all local extrema, then select all of the following that are true of f. Select all that apply: f has a local maximum at x=1/3. f has a local maximum at x=2/3. f has a local minimum at x=1/3. f has a local minimum at x=2/3.

For the function f(x,y) = 4xy - x^3 - 2y^2 find and label any relative extrema...

For the function f(x,y) = 4xy - x^3 - 2y^2 find and label any relative extrema or saddle points. Use the D test to classify. Give your answers in (x,y,z) form. Use factions, not decimals.

Find and classify the local extrema of the function f(x,y) = (x^3)y+12(x^2)+16(y^2).

1. Use the derivative function, f'(x)f′(x), to determine where the function f(x)=−2x^2+14x−8 is increasing. 2.Use the...

1. Use the derivative function, f'(x)f′(x), to determine where the function f(x)=−2x^2+14x−8 is increasing. 2.Use the derivative function f'(x)f′(x) to determine where the function f(x)=2x^3−27x^2+108x+13 is increasing. 3.Use the derivative function f'(x)f′(x) to determine where the function f(x)=2x^3−27x^2+108x−12 is decreasing. 4.Find each value of the function f(x)=−x^3+12x+9 where the line tangent to the graph is horizontal. x=

Find the local extrema of the following function. f(x,y)=108+7xy-5x2-6y2

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable....

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable. (If an answer does not exist, enter DNE.) g(x)=x^3-6x relative maximum (x, y) = ( , ) relative minimum (x, y) = ( , )

1. Determine the absolute minimum and maximum values of the function f(x) = x^3 - 6x^2...

1. Determine the absolute minimum and maximum values of the function f(x) = x^3 - 6x^2 + 9x + 1 in the following intervals: a) [0,5] b) [-1,2] 2. A company produces and sells x number of calculators per week. The functions for demand and cost are the following: p = 500 - 0.5x and c(x) = 10,000 + 135x. Determine: a) Function of weekly revenue b) Price and number of calculators that have to be sold to maximize revenue...

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and...

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and use it to graph the function. Find: a)(2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e)(4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve

f(x) = 10/cos-1(x). Use calculus to determine: a) all critical values b) any local extrema c)...

f(x) = 10/cos-1(x). Use calculus to determine: a) all critical values b) any local extrema c) any absolute extrema d) the intervals where f is increasing/decreasing e) any points of inflection rounded to the thousandths place f) intervals where f is concave up/down No interval was specified so I assumed 0<x<2pi also I didn't get any concavity not sure if I'm right or not. I got x= pi as the critical value as well as the relative and absolute minimum...

Find the relative extrema, if any, classify as absolute max/min. a.) f(x)= x+1/x-2 on [2,4] b.)...

Find the relative extrema, if any, classify as absolute max/min. a.) f(x)= x+1/x-2 on [2,4] b.) f(x)= x^(2) -2x-3 on [-2,3] c.) f(x)= x^(2/3) (x^2-4) on [-1,3] Solve for x: a.) 6^(2x) =36 b.) 2^(2x) -4 * 2^(x) +4=0 c.) 3^(x-x^2) =1/9x Determine if the following statements are true or false. If it is true, explain why. If it is false, provide an example. a.) If a and b are positive numbers, then (a+b)^x=a^x+b^x b.) If x < y, then...

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