suppose that 3 <_ f prime of x <_ 5, for all values x. show that 18<_ f(8)f(2) <_ 30
<_ signs mean less or equal to...
im supposed to apply mean value theorem or rolle's theorem... i don't understand neither so i cant do the question! please help!
 👍
 👎
 👁
 ℹ️
 🚩
1 answer

If f'=3, then f=3x+C, so f(8)]=24+C, but C=2 if f'=3. So f(8)=26
f(2)=8 by the same argument.
then if f'x=3, f(8)f(2)=268=>18
You can make the same logic if f'=5, solve for C, then show that f(8)f(2)<=30 👍
 👎
 ℹ️
 🚩
👤bobpursley
Answer this Question
Related Questions

trig
Scientists believe that the average temperature at various places on Earth vary from cooler to warmer over thousands of years of gradual climate change. Suppose that at one place, the highest avg temp is 80 and the lowest is 60. Also suppose that the time

Probability
1.Let 𝑋 and 𝑌 be two binomial random variables: a.If 𝑋 and 𝑌 are independent, then 𝑋+𝑌 is also a binomial random variable b.If 𝑋 and 𝑌 have the same parameters, 𝑛 and 𝑝 , then 𝑋+𝑌 is a binomial random variable c.If 𝑋

Calculus
Suppose f(pi/3) = 3 and f '(pi/3) = −7, and let g(x) = f(x) sin x and h(x) = (cos x)/f(x). Find the following. a. g'(pi/3) b. h'(pi/3)

Algebra 1
suppose y varies directly with x and y = 14 when x = 4 what is the value of y when x = 6

finite math
Suppose that E and F are two events P(E and F)=0.1 and P(E)=0.4 what is P(F/E)?

physics
EXERCISE 4.9 (a) Suppose a hockey puck slides down a frictionless ramp with an acceleration of 5.00 m/s2. What angle does the ramp make with respect to the horizontal? (b) If the ramp has a length of 6.00 m, how long does it take the puck to reach the

algebra
Suppose p and q are inversely proportional. If p=28 when q=7, find the value of p when q= 49.

Probability
For each of the following statements, state whether it is true (meaning, always true) or false (meaning, not always true): 1. Let X and Y be two binomial random variables. (a) If X and Y are independent, then X+Y is also a binomial random variable. (b) If

Algebra
Suppose that ab+bc+ca=20. What is the maximum possible value of ab?

Probability
Let X and Y be independent positive random variables. Let Z=X/Y . In what follows, all occurrences of x , y , z are assumed to be positive numbers. 1) Suppose that X and Y are discrete, with known PMFs, pX and pY . Then, pZY(zy)=pX(?). What is the

math
Suppose a company has fixed costs of $45,600 and variable cost per unit of 1/3x + 444 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 2368 − 2/3x dollars per unit. (a) Find the breakeven

physics
A runner covers one lap of a circular track 40.0 m in diameter in 62.5 s. Suppose initially the runner starts by going in the north direction. Assume the speed is constant for the first halflap and then constant for the 2nd halflap. Suppose instead the

Probability
1. Suppose three random variables X , Y , Z have a joint distribution PX,Y,Z(x,y,z)=PX(x)PZ∣X(z∣x)PY∣Z(y∣z). Then, are X and Y independent given Z? 2.Suppose random variables X and Y are independent given Z , then the joint distribution must be of

AP Algebra 8th grade
Suppose U = {1,2,3,4,5,6,7,8}, Is the Universal set, and P = {1,3,5,7}, What is P' A) {2,4,6,8} B) {1,2,3,4,5,6,7,8} C) {1,3,5,7} D) {1,3,5,7,8} I think A.

Calculus
Suppose g (x) is increasing and concave up everywhere and g (A) = 9, g '(A) = 17, h = 0.01 estimate g(Ah)

chemistry
Suppose you are asked to find the area of a rectangle that is 2.1cm \rm cm wide by 5.6cm \rm cm long. Your calculator answer would be 11.76 cm 2 \rm cm^2 . Now suppose you are asked to enter the answer to two significant figures. (Note that if you do not

Calculus
1. Suppose C(x) is a function representing the cost (in dollars) of producing x units of energy, and R(x) is a function representing the revenue (in dollars) of selling x units of energy. Suppose further that both functions are continuous for all x > = 0.

Chemistry
Suppose you had a mixture consisting of 20.0 g of compound A and 20.0 g of compound B dissolved in 100.0 mL of water at 95 degrees C. Suppose further that only 1.00 g of A are soluble in 100.0 mL of water at 5 degrees C but 15.0 g of B are soluble in 100.0

math
suppose u = (1, 2, 3, 4, 5, 6, 7, 8) is the universal set and p = (1, 2, 3, 4). what is p? a.) (5, 6, 7, 8)*** b.) (1, 2, 3, 4, 5, 6, 7, 8) c.) (1, 2, 3, 4) d.) cannot be determined i think it's a.) (5, 6, 7, 8) am i right?

Maths
Suppose that R is at (8, 6). Let P be a point on the line 8y = 15x and Q be a point on the line 10y = 3x, and suppose that R is the midpoint of PQ. Then the length of PQ can be written as a / b, where a and b have no common factors other than 1. What is a
Still need help?
You can ask a new question or browse existing questions.