Real Analysis : Points on a Differentiable Function
Not what you're looking for?
Let h be a differentiable function defined on the interval [0,3], and assume that h(0)=1 h(1)=2 and h(3)=2.
a- argue that there exists a point d belong to [0,3] where h(d)=d.
b-argue that at some point c we have h'(c)=1/3.
c-argue that h'(x)=1/4 at some point in the domain.
Purchase this Solution
Solution Summary
Points on a differentiable function are investigated in the solution.
Solution Preview
Proof:
a. Let f(x)=h(x)-x. Then we have f(0)=h(0)-0=1-0=1>0, f(3)=h(3)-3=2-3=-1<0. According to the Intermeidate Value Theorem, we can find some d in [0,3], such that f(d)=0. This implies h(d)-d=0, so ...
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Probability Quiz
Some questions on probability
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.