Question

Identify the critical points and find the maximum and minimum of the given function on the given interval I.

a) G(x) = (1/5)(2x^3 +3x^2−12x); I = [−3,3]
b) g(x) = 1/(1+x^2); I = [−3,1]
c) f(x) =x/(1+ x^2); I = [−1,4]
d) a(t) = cost; I = [π,5π]

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: approximate the area under the graph of f(x) and above the x-axis using the following methods with n...

A: Given:The function is f(x) = ex-1.The interval (a, b) is (0,1)

Q: If a cup of coffee has temperature 95°C in a room where the temperature is 20°C, then, according to ...

A: The equation for the temperature of the coffee after t minutes is,

Q: Determine the interval(s) on which the following function is continuous, then analyze the given limi...

A: (2+2cosx) and sinx both are continuous functions. So the function (2+2cos x)/sinx will be discontinu...

Q: If y (in 2)2, then O 2eln 2 0 O 2 In 2 1 (in 2)2 O eln 2

A: We have to find derivative of y .Question is given below:

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by th...

A: (d) First draw the graph of y = x + 6 and y = x2.Find the intersection points as,

Q: Hello,  I need help explaining how pi(k)/2 came about, I know where pi/4 came from. Thank you for th...

A: Consider the provided trigonometry equation.

Q: How can I get the result? Which is the result

A: To find two positive numbers whose sum is 210 and whose product is a maximum.(a) Analytically comple...

Q: How to convert percentage to ratio?

A: In this question we have to explain how to convert the percentage in fraction form.

Q: The function s(x) = 3600/(60 + x) = 3600(60 + x)^-1 gives a person's average speed in miles per hour...

A: The function of distance,

Q: Determine the radius of convergence of the following power series. Then test the endpoints to determ...

A: The power series is given as

Q: Please help me about this.

A: The radius of convergence is 4 which can be computed as follows.

Q: e2h-1 if f'(a) lim-0 what is f(r) and what is a? h

A: Click to see the answer

Q: Activity 5 Inverse Functions and their Derivatives 10. When a camera flash goes off, the batteries i...

A: Given:The function is Q(t) = Q0(1−e−t/a), where t is the time in seconds and Q0  is the maximum char...

Q: 5 dx In 26 In 24 '을 In 24 글 In 26 none of the above

A: Obtain the value of the integral as follows.

Q: Calculus Question

A: The given curve is,

Q: y′=−3x+9 Determine the particular solution to the differential equation that passes through the poin...

A: The given differential equation is y’ = –3x+9.

Q: 1) The substitution u = tanx gives∫(sec2x.tanx)dx = ∫(x)du = 1/2.u2 + C = 1/2.tan2x + CThe substitut...

A: Yes, both integrations are correct by their respective substitutions.Reason:An integral of a functio...

Q: graph quadratic function f(x) = -3x2- 12x -1

A: Consider the given equation

Q: Find the position and velocity of an object moving along a straight line with the given  acceleratio...

A: Obtain the velocity  as follows.

Q: Calculate the area, in square units, bounded above by f(x)=−2x2 −x−21 and below by g(x)=−x2 −12x+9.

A: Click to see the answer

Q: How do you set up the integral?

A: Given a triangle with function and the vertices,

Q: 150 100 50 20 40 60 3. Suppose that a population develops according to the logistic equation (c) Use...

A: Given that a population develops according to the logistic equation

Q: Find the flux of the following vector field across the given surface with the specified orientation....

A: Let r be the vector on the surface of  the cylinder y=6x2 for 0 ≤ x ≤ 4​, 0 ≤ z ≤ 2​.Let's parameter...

Q: Suppose that the cost funtion for a commodity is  C(x)= 300+6x+1/20x^2 dollars (a) Find the marginal...

A: The given Cost function for a commodity is C(x) = 300 + 6x + (1/20)x2.(a) To find the marginal cost ...

Q: How can I get the result?

A: We used a calculator to find the values for the table.  And rounded each value to 4 decimal places. ...

Q: curves. Find the volume of the solid generated when R is revolved about the x-axis Let R be the regi...

A: Use disk method to find the volume of the solid generated when R is revolved about the x-axis is cal...

Q: Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by abo...

A: Click to see the answer

Q: I need help about solving this problem. a) How do I find the time required to reach the maximum amou...

A: Let F be the amount of fertilizer. In 1 minute 1 gallon of solution comes in and 5 gallons of soluti...

Q: #28 please

A: The given function of hyperbola can be written in terms of y as: Plugging this value in the objectiv...

Q: Find the exact value of log10(15/4)+log10(4000/15)

A: Given information:The given expression is  

Q: Use the derivative f'(x) = (x - 3)(x + 4)(x + 4) to determine the maxima and minima of f and the int...

A: f will be increasing if f'(x)>0. From the graph of f'(x) we see f'(x)>0 when x>3 [because a...

Q: G(x) = ∫^1vx xt2 dt (1 is the number on top of the integral sign, x on the bottom)

A: Given integral is:Solving the indefinite integral: The antiderivative of a function of the form xn i...

Q: dy Ify드a2-4x-의. then. dx x2 2x-2) 2-4x-5 einz2-4x-5)- In(z+2)]. x2-4x-5 x2 x2-4x-5 x 2 x 2 2-4x-5 x2...

A: Consider the given equation:

Q: Use Newton's method to approximate all intersection points of the following pair of curves. Round to...

A: Before we get into the solution of the question, let's understand a bit about Newton's method. If xn...

Q: A port and a radar station are 3 mi apart on a straight shore running east and west. A ship leaves t...

A: Please look at thediagram on white board. I have used the diagram from the question itself and marke...

Q: I need help on how to contruct the definite integral needed to find the area of the geometric shape ...

A: Formula of area of triangle is = (1/2)*b*h, where b=base, h=height 

Q: b. Find the area of the region bounded by Y = xe ax and the x-axis on the interval 0,41, where a> 0....

A: Area of region which is bounded by f(x) and x-axis on [0,4] computed as follows.

Q: Logarithmic differentiation

A: The given function is y=(x+1)²(x-2)(x²+3).

Q: For the year data given in the chart find a power function that is used to model the Lorenz function...

A: A power function is of the form,y = axbWe can take log to the natural base “e” on the both the sides...

Q: Evaluate the integral.   Integral from nothing to nothing hyperbolic cotangent StartFraction x Over ...

A: Refer to the integral,Rewrite the hyperbolic cotangent as,

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they ...

A: The given interval is [-1,1] and the function is,   

Q: k 5k! x Find the radius of convergence of- (2kk The radius of convergence is Type an exact answer in...

A: We have to find radius of convergence of series.Series is given below:

Q: Sketch the region of integration and evaluate the following integrals. Please refer to attached imag...

A: Click to see the answer

Q: If y x4x+3, then 2ix+3ix3 2i 3ix3 O (4x+1)/4x+3 2Ax+3 2x vi3Ar3

A: The function is given by,

Q: How can I get the result? Which is the result?

A: The definite integral is given by,

Q: Calculate the area, in square units, bounded by g(x)=4x−2 and f(x)=5x−15 over the interval [−11,4]. ...

A: Area of region between g(x) and f(x) over the interval [–11,4] is computed as follows.

Q: Help please..

A: The general Taylor series for ex at x = 0 is as follows.

Q: Please help!

A: Recall the quotient rule for derivative:

Q: If given the differential equation y''-4y'+4y=et, is there a way to solve it for possible solutions?...

A: we are given a differential equation as  

Q: y′=−2ex −9x2 +x+4 y(0)=6 Solve the initial value problem above. Do not include "y=" in your answer.

A: Solve the Initial Value Problem(IVP) for first degree differential equation is given.