Homework Help: calculus

Posted by michael on Thursday, November 12, 2009 at 1:31am.

Consider the function f(x)=4sqrtx+5 on the interval [4,5]. Find the average or mean slope of the function on this interval.
By the Mean Value Theorem, we know there exists a c in the open interval (4,5) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

calculus - drwls, Thursday, November 12, 2009 at 1:49am
1) For the average value of the SLOPE of f(x) in that interval, calculate Integral of f'(x) from 4 to 5. You have to divide by the interval to get the average, but that is 1.

f'(x) = 2/sqrtx
Average value = INTEGRAL 2 x^-1/2 dx
from 4 to 5

= 4 (sqrt 5 - sqrt 4) = 0.9443

2) Now that you have the average value of f'(x), find the value of c such that f'(c) = f'(x)(average)

2/sqrtc = 0.9443
sqrt c = 2.118
c = 4.486

Answer this Question

Related Questions

calculus - Consider the function f(x)=–3x3–1x2+1x+1Find the average ...
math - Consider the function f(x)=2sqrtx+4 on the interval [2,8]. Find the ...
calculus - Consider the function f(x)=6sqrt(x)+1 on the interval [3,5] . Find ...
CALCULUS! - Consider the function f(x)=4x^3–2x on the interval [–2,2...
calculus - Consider the function f(x)=3x^2 – 5x on the interval [-4,4]. ...
calc - consider the function f(x)=x^3 - x^2 - 3x -2. find the average slope of ...
math - Consider the function f(x)=–2x^3–3x^2+2x–2 Find the ...
Calculus - Find the average or mean slope of 2x^3 - 6x^2 - 90x +3 on the ...
Calc, Mean Value Theorem - Consider the function : 3x^3 - 2x^2 - 4x + 1 Find the...
Math - Consider the function f(x)=8(x^(1/2))+7 on the interval [1,5]. By the ...

For Further Reading

First Name:
School Subject:
Answer: