Question

Given a continuous function f on [0, 1]. Suppose f'(0) and f''(0) both exits on (0,...

Given a continuous function f on [0, 1]. Suppose f'(0) and f''(0) both exits on (0, 1). Determine whether the following general statements about f are true or not. If not, give a counter-example

1. Suppose f(1/2) is a local extreme value of f, then f'(1/2) = 0?

2. Suppose f '( 1 2 ) = 0, then f(1/2) is a local extreme value of f.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose f is continuous on (−∞,∞), and the derivative satisfies: f' (x) < 0 on (−∞,...
Suppose f is continuous on (−∞,∞), and the derivative satisfies: f' (x) < 0 on (−∞, −2) ∪ (3,∞) and f' (x) > 0 on (−2, 3). What can you say about the local extrema of f?
Suppose f is a function with f(1) = f′(1) = ··· = f^(9) (1) = 0,...
Suppose f is a function with f(1) = f′(1) = ··· = f^(9) (1) = 0, f^(10) (1) = −2, and f^(11) (1) = 3. Write the 11-th Taylor polynomial of f at a = 1, and determine if f has a local maximum or a local minimum or neither at 1.
Define g(x) = f(x) + tan-1 (2x) on [−1, √3/2 ]. Suppose that both f'' and...
Define g(x) = f(x) + tan-1 (2x) on [−1, √3/2 ]. Suppose that both f'' and g'' are continuous for all x-values on [−1, √3/2 ]. Suppose that the only local extrema that f has on the interval [−1, √3/2 ] is a local minimum at x = 1/2 . (a) Determine the open intervals of increasing and decreasing for g on the interval [1/2 , √3/2] . (b) Suppose f(1/2) = 0 and f(√3/2) = 2. Find the absolute...
The probability density function for a continuous random variable X is given by         f(x) = 0.6                 0<X<1...
The probability density function for a continuous random variable X is given by         f(x) = 0.6                 0<X<1               = 0.10(x)         1 ≤X≤ 3               = 0 otherwise Find the 85th percentile value of X.
Probability density function of the continuous random variable X is given by f(x) = ( ce...
Probability density function of the continuous random variable X is given by f(x) = ( ce −1 8 x for x ≥ 0 0 elsewhere (a) Determine the value of the constant c. (b) Find P(X ≤ 36). (c) Determine k such that P(X > k) = e −2 .
Give an example or explain why the request is impossible. A function f(x) that is continuous...
Give an example or explain why the request is impossible. A function f(x) that is continuous at 0 and g(x) that is not continuous at 0 such that f(x) - g(x) is continuous at 0.
For the given function: f [0; 3]→R is continuous, and all of its values are rational...
For the given function: f [0; 3]→R is continuous, and all of its values are rational numbers. It is also known that f(0) = 1. Can you find f(3)?Justification b) Let [x] denote the smallest integer, not larger than x. For instance,[2.65] = 2 = [2], [−1.5] =−2. Caution: [x] is not equal to |x|! Find the points at which the function f : R→R. f(x) = cos([−x] + [x]) has or respectively, does not have a derivative.
Does there exist a continuous onto function f : [0, 1] → R? Does there exist...
Does there exist a continuous onto function f : [0, 1] → R? Does there exist a continuous onto function f : (0, 1) → (−1, 0) ∪ (0, 1)?
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...
If f is a continuous, positive function defined on the interval (0, 1] such that limx→0+...
If f is a continuous, positive function defined on the interval (0, 1] such that limx→0+ = ∞ we have seen how to make sense of the area of the infinite region bounded by the graph of f, the x-axis and the vertical lines x = 0 and x = 1 with the definition of the improper integral. Consider the function f(x) = x sin(1/x) defined on (0, 1] and note that f is not defined at 0. • Would...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT