Asked Apr 5, 2019

Identify the absolute minimum of g(x)=−2x2 −x+1 over [−2,4].


Expert Answer

Step 1

Absolute minimum:

The absolute minimum of a function f on the interval [a, b] will occur either at the endpoints [a, b] or at a critical point of f in [a, b]. That is, f’(c) = 0 for some c where a < c < b.

Step 2

Obtain the critical point of the function g(x) in [–2, 4]:

The given function is g(x) = –2x2x +1.

The given interval is [–2, 4].

The critical point of the function g(x) in [–2, 4] is obtained as (–1/4) from the calculation given below:

Step 3

Obtain the absolute minimum of the function g(x) in [–2, 4]:

Now substitute the values –2, –1/4, 4 for x in the function g(x) = –2x2 – x +1.

The absolute minimum of th...


Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in



Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A

Q: Please help me solve this differential equation and identify P(x), Q(x) and v(x).

A: First we rearrange the equation and find P(x) and Q(x)


Q: Logarithmic differentiation see below

A: The given function is ,


Q: 4. Two stationary patrol cars equipped with radar are 6 miles apart on a highway. A truck passes a p...

A: Using Mean value theoremt,to calculate the speed limit of the truck driver passing the second patrol...


Q: How do I solve this Bernoulli equation using P(x), Q(x) and n as well as u(y)?

A: First, we write it in form of Bernoulli Differential equation. 


Q: Find the average value of the function f(x) = e-4x on the interval [0, 1/2].   please show and expla...

A: The function is given by,


Q: For the sequence 1, 4, 7, 10,..., its nth term is Preview My Answers Submit Answers ou have attempte...

A: The given sequence is 1,4,7,10, ...


Q: Evaluate the following integral as written. Please refer to attached image.

A: It's  aquestion of double integral. We will first evalaute the integral with respect to x, put the l...


Q: An object is thrown straight up with a velocity, in ft/s, given by v(t)32t +53, where t is in second...

A: a)The given velocity function is v(t) = −32t + 53.In order to find the initial velocity, substitute ...


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,