Mean Value Theorem for Continuous Functions - Page 5
Questions
- How do you verify that the hypotheses of the Mean-Value Theorem are satisfied on the interval [-3,0] and then find all values of c in this interval that satisfy the conclusion of the theorem for # f(x) = 1/(x-1)#?
- How do you use the Intermediate Value Theorem to show that the polynomial function #f(x)=3x-2sin(x)+7# has one zero?
- How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = x^3 -3x^2 + 3# has one zero?
- Given the function #f(x)=5-4/x#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,4] and find the c in the conclusion?
- How do I find the numbers #c# that satisfy Rolle's Theorem for #f(x)=cos(2x)# on the interval #[pi/8,(7pi)/8]# ?
- How do you determine if Rolles Theorem applies to the given function #x^3 - 9x# on [0,3]. If so, how do you find all numbers c on the interval that satisfy the theorem?
- How do you know whether Rolle's Theorem applies for #f(x)=x^2/3+1# on the interval [-1,1]?
- Given the function #f(x) = x^3 + x - 1#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0,4] and find the c?
- In the following graph, how do you determine the value of c such that #lim_(x->c) f(x)# exists?
- Does the function #f(x) = 2x^2 − 5x + 1# satisfy the hypotheses of the Mean Value Theorem on the given interval [0,2]?
- How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [-1,1] for #f(x) = x(x^2 - x - 2)#?
- How do you find all numbers c in the interval show that the function #f(x)=x^3+x+1# satisfies the mean value theorem on the interval [-1,2]?
- How do you determine whether the Mean Value Theorem can be applied to #f(x) = sqrt (x-7)# on the interval [11,23]?
- Does rolle's theorem apply for #f(x) = abs(x-2)# on [0,4]?
- How do you find the number c that satisfies the conclusion of Rolle's Theorem for #f(x) = cos(5x)# for [π/20,7π/20]?
- Given the function #f(x)=-x^2+8x-17#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [3,6] and find the c?
- How do you use the Intermediate Value Theorem to show that the polynomial function #sin2x + cos2x - 2x = 0# has a zero in the interval [0, pi/2]?
- Given the function #f(x)=-(-2x+6)^(1/2)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-2,3] and find the c?
- Given the function #f(x)=x/(x+9)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,18] and find the c?
- Use limits to verify that the function #y=(x-3)/(x^2-x)#has a vertical asymptote at #x=0#? Want to verify that #lim_(x ->0)((x-3)/(x^2-x))=infty#?