Question

If f(2) = 5 and f '(x) ≥ 1 for 2 ≤ x ≤ 6, how...

If f(2) = 5 and f '(x) ≥ 1 for 2 ≤ x ≤ 6, how small can f(6) possibly be?

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

If f is continuous on [a,b] and differentiable on (a,b) then according to mean value theorem there exists c in (a,b) such that,

Let's assume that f is continuous on [2,6] and differentiable on (2,6) then according to mean value theorem there exists c in (2,6) such that,

Hence we can say that,

we have f(2) = 5 hence,

The smallest value of f(6) possibly be 9

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
If f(4) = 5 and f '(x) ≥ 3 for 4 ≤ x ≤ 9, how...
If f(4) = 5 and f '(x) ≥ 3 for 4 ≤ x ≤ 9, how small can f(9) possibly be?
If  f ″(x)  =  (x − 1)^5 (x − 2)^7 (x − 3)^6, how many inflection...
If  f ″(x)  =  (x − 1)^5 (x − 2)^7 (x − 3)^6, how many inflection points does  f (x) have
1. If f(x) = ∫10/x t^3 dt then: f′(x)= ? and f′(6)= ? 2. If f(x)=∫x^2/1...
1. If f(x) = ∫10/x t^3 dt then: f′(x)= ? and f′(6)= ? 2. If f(x)=∫x^2/1 t^3dt t then f′(x)= ? 3. If f(x)=∫x3/−4 sqrt(t^2+2)dt then f′(x)= ? 4. Use part I of the Fundamental Theorem of Calculus to find the derivative of h(x)=∫sin(x)/−2 (cos(t^3)+t)dt. what is h′(x)= ? 5. Find the derivative of the following function: F(x)=∫1/sqrt(x) s^2/ (1+ 5s^4) ds using the appropriate form of the Fundamental Theorem of Calculus. F′(x)= ? 6. Find the definitive integral: ∫8/5...
Given f ' ' ( x ) = 2 x + 6 and f ' (...
Given f ' ' ( x ) = 2 x + 6 and f ' ( − 2 ) = 5 and f ( − 2 ) = 2 . Find f ' ( x ) and find f ( 1 )
Let f(x)=ln[x^3(x+5)^5(x^2+4)^6] f '(x)=
Let f(x)=ln[x^3(x+5)^5(x^2+4)^6] f '(x)=
1) Find the antiderivative if f′(x)=x^6−2x^−2+5 and f(1)=0 2)Find the position function if the velocity is...
1) Find the antiderivative if f′(x)=x^6−2x^−2+5 and f(1)=0 2)Find the position function if the velocity is v(t)=4sin(4t) and s(0)=0
Verify the quotient rule for each of the following: 1. f(x)=4x^5-4x^4+13x^3-2x^2+7x+6/x^2-x+2 2.  f(x)=20x^8-28x^6+29x^4-35x^2+5/5x^4-7x^2+1
Verify the quotient rule for each of the following: 1. f(x)=4x^5-4x^4+13x^3-2x^2+7x+6/x^2-x+2 2.  f(x)=20x^8-28x^6+29x^4-35x^2+5/5x^4-7x^2+1
5. Part I If f(x) = 2x 2 - 3x + 1, find f(3) - f(2)....
5. Part I If f(x) = 2x 2 - 3x + 1, find f(3) - f(2). A. 0 B. 7 C. 17 Part II If G( x ) = 5 x - 2, find G-1(x). A. -5x + 2 B. (x + 2)/5 C. (x/5) + 2 Please help me solve this problem and if you can please also show or explain how you got that answer. Thank you! :)
Find the function f(x) such that f′′(x)=12x^2− 2/x^2 and f(1) = 5, f′(1) = 2
Find the function f(x) such that f′′(x)=12x^2− 2/x^2 and f(1) = 5, f′(1) = 2
1. 4(x+1)^2+5(x+1)-8 = 4(-x)^2+5(-x)-8= 4(x^3)^2+5(x^3)-8= 2. f(x)= { x^2 if x<0.   x+9 if x>=0} f(-2) =...
1. 4(x+1)^2+5(x+1)-8 = 4(-x)^2+5(-x)-8= 4(x^3)^2+5(x^3)-8= 2. f(x)= { x^2 if x<0.   x+9 if x>=0} f(-2) = f(-1) = f(0)= f(1)= f(2)= 3. f(x)= {x^2 +8x if x<= -1. X If -1< x<=1. -1 if x>b1} F(-3)= F(-3/2)= F(-1) = F(40) = 4. F(x)= 6x-7 f(2x)= 2f(x)=
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT