Question

         Suppose f(x) is a function and that c is a critical number for f(x) at...

         Suppose f(x) is a function and that c is a critical number for f(x) at which both f' and f'' are defined. Write a paragraph explaining exactly what the Second Derivative Test allows us to conclude about the point where x = c.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. What is a critical number of a function f ? What is the connection between...
1. What is a critical number of a function f ? What is the connection between critical numbers and relative extreme values? 2. What does the sign of the derivative, f ', tell us about the function? What does the sign of the 2nd derivative, f ", tell us about the function?
Find the critical point of the function f(x,y)=x2+y2+xy+12x c=________ Use the Second Derivative Test to determine...
Find the critical point of the function f(x,y)=x2+y2+xy+12x c=________ Use the Second Derivative Test to determine whether the point is A. a local maximum B. a local minimum C. a saddle point D. test fails
Problem 1. (1 point) Find the critical point of the function f(x,y)=−(6x+y2+ln(|x+y|))f(x,y)=−(6x+y2+ln(|x+y|)). c=? Use the Second...
Problem 1. (1 point) Find the critical point of the function f(x,y)=−(6x+y2+ln(|x+y|))f(x,y)=−(6x+y2+ln(|x+y|)). c=? Use the Second Derivative Test to determine whether it is A. a local minimum B. a local maximum C. test fails D. a saddle point
Given the function h(x)=e^-x^2 Find first derivative f ‘ and second derivative f'' Find the critical...
Given the function h(x)=e^-x^2 Find first derivative f ‘ and second derivative f'' Find the critical Numbers and determine the intervals where h(x) is increasing and decreasing. Find the point of inflection (if it exists) and determine the intervals where h(x) concaves up and concaves down. Find the local Max/Min (including the y-coordinate)
Let f(x) = 4x^5 − 5x^4 + 9. (a) Find each critical number for f. (b)...
Let f(x) = 4x^5 − 5x^4 + 9. (a) Find each critical number for f. (b) Apply the First Derivative Test to each critical number found in part (a), being careful to explain what conclusions (if any) you can draw. (c) Apply the Second Derivative Test to each critical number found in part (a), being careful to explain what conclusions (if any) you can draw.
f(x)=x^3-4x^2+5x-2 Find all critical numbers of the function, then use the second derivative test on each...
f(x)=x^3-4x^2+5x-2 Find all critical numbers of the function, then use the second derivative test on each critical number to determine if it is a local maximum or minimum. Show your work.
a) The function f(x)=ax^2+8x+b, where a and b are constants, has a local maximum at the...
a) The function f(x)=ax^2+8x+b, where a and b are constants, has a local maximum at the point (2,15). Find the values of a and b. b) if b is a positive constand and x> 0, find the critical points of the function g(x)= x-b ln x, and determine if this critical point is a local maximum using the second derivative test.
Consider the following function. f (x, y)  =  (x − 6) ln(x5y) (a) Find the critical...
Consider the following function. f (x, y)  =  (x − 6) ln(x5y) (a) Find the critical point of  f. If the critical point is (a, b) then enter 'a,b' (without the quotes) into the answer box. (b) Using your critical point in (a), find the value of D(a, b) from the Second Partials test that is used to classify the critical point. (c) Use the Second Partials test to classify the critical point from (a). one of: relative max, relative...
Consider the function f(x) = x^2/x-1 with f ' (x) = x^2-2x/ (x - 1)^2 and...
Consider the function f(x) = x^2/x-1 with f ' (x) = x^2-2x/ (x - 1)^2 and f '' (x) = 2 / (x - 1)^3 are given. Use these to answer the following questions. (a) [5 marks] Find all critical points and determine the intervals where f(x) is increasing and where it is decreasing, use the First Derivative Test to fifind local extreme value if any exists. (b) Determine the intervals where f(x) is concave upward and where it is...
f(x)=5x^(2/3)-2x^(5/3) a. Give the domain of f b. Find the critical numbers of f c. Create...
f(x)=5x^(2/3)-2x^(5/3) a. Give the domain of f b. Find the critical numbers of f c. Create a number line to determine the intervals on which f is increasing and decreasing. d. Use the First Derivative Test to determine whether each critical point corresponds to a relative maximum, minimum, or neither.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT