Question

Determine whether Rolle's Theorem can be applied to the function f(x) = x^4-2x^2 [-2,2]. if not...

Determine whether Rolle's Theorem can be applied to the function f(x) = x^4-2x^2 [-2,2]. if not find c and explain why

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

We are given that a function

Interval:[-2,2]

Rolle's theorem: It stats that the function is continuous on closed interval [a,b] and differentiable on (a,b) such that

f(a)=f(b) ,then f'(c)=0 for some

Given function is polynomial .Therefore, the function is defined on interval [-2,2].

It is differentiable on (-2,2) because derivative exist.

Therefore,Rolle's theorem can be applied.

When Rolle's theorem applies then there exits c such that

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
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select...
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = cos x,    [π, 3π] Yes. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). No, because f(a) ≠ f(b). If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f '(c) = 0. (Enter your answers...
Can the Mean Value Theorem can be applied to the function f(x)=(5x-2)/(x+1) on the interval [-2,2]?...
Can the Mean Value Theorem can be applied to the function f(x)=(5x-2)/(x+1) on the interval [-2,2]? Fully explain why or why not.
Determine whether Rolle’s Theorem can be applied to f on the given interval. If Rolle’s Theorem...
Determine whether Rolle’s Theorem can be applied to f on the given interval. If Rolle’s Theorem can be applied, find all the values of c in the interval (a, b) such that f 0 (c) = 0. If Rolle’s Theorem cannot be applied, explain why. h(x) = x 2 − 2x/ x + 2 on [−1,6]
# 12 In Exercises 9–12, determine whether Rolle’s Theorem can be applied to f on the...
# 12 In Exercises 9–12, determine whether Rolle’s Theorem can be applied to f on the closed interval [a, b]. If Rolle’s Theorem can be applied, find all values of c in the open interval (a, b) such that f ′(c) = 0. If Rolle’s Theorem cannot be applied, explain why not. 12. f (x) = sin 2x, [−π, π]
Determine whether the Mean Value Theorem can be applied to ?(?) = ?^3 − 3? +...
Determine whether the Mean Value Theorem can be applied to ?(?) = ?^3 − 3? + 2 on the closed interval [−2,2]. If the Mean Value Theorem can be applied, find all values of ?? in the open interval (−2,2) such that ?′ (?) = ?(2) − ?(−2) /2 − (−2) If the Mean Value Theorem cannot be applied, explain why not.
determine whether​ Rolle's Theorem applies to the following function on the given interval. If​ so, find...
determine whether​ Rolle's Theorem applies to the following function on the given interval. If​ so, find the​ point(s) that are guaranteed to exist by​ Rolle's Theorem.​g(x)=x^3 + 7 x ^2 - 5 x - 75​; ​[- 5​,3​]
1. Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval....
1. Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 7 − 24x + 2x^2, [5, 7]
1) Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval....
1) Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 1 − 12x + 2x^2, [2, 4] c = 2) If f(2) = 7 and f '(x) ≥ 1 for 2 ≤ x ≤ 4, how small can f(4) possibly be? 3) Does the function satisfy the hypotheses of the Mean Value Theorem...
Determine whether the Mean Value theorem can be applied to f on the closed interval [a,...
Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f (x) = x7, [0,1] Yes, the Mean Value Theorem can be applied. No, f is not continuous on [a, b]. No, f is not differentiable on (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f ‘(c) = f (b)...
Determine whether the Mean Value theorem can be applied to f on the closed interval [a,...
Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 8 − x ,    [−17, 8] Yes, the Mean Value Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT