Mean Value Theorem for Continuous Functions - Page 13

  • Find a continuous solution of the IVP dy/dt+y=g(t),y(0)=0 where g(t)=[2,0≤t≤1 0,t>1.?
  • Consider the function 1-7x^2 on the interval [-2, 7]. How do I find the average slope on this interval? Find the one point in which f'(c) is equal to the mean slope.
  • Does the function f(x)=#sqrtx# satisfy the hypothesis of the Mean Value Theorem on the closed interval [0,4]? Then find all numbers c that satisfy the conclusion of the Mean Value Theorem
  • When will the slope field for the differential equation #dy/dx=(yx^2+xy^2)/(3x+y)# have horizontal segments?