Purchase Solution

Application of Rolle's theorem - Intercepts

Not what you're looking for?

Ask Custom Question

Please state whether the statements are true or false, and if false, why.

If the graph of a function has three x intercepts, then it must have at least two points at whch its tangent line is horizontal.

If f'(x) = 0 for all x in the domain of f, then f is a constant function.

Purchase this Solution
Solution Summary

This solution explains the connection between the number of x-intercepts and horizontal tangents.

Solution Preview

Suppose the graph has three x intercepts (assuming that the graph has amooth and no holes in it. in other words, the function is continuous and differentiable) which means the graph is cutting the x-axis in four points ...

Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

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.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Calculus/ For OTA 103997 only

    Decide whether Rolle's Theorem can be applied to on the interval [-1,3]. If Rolle's Theorem can be applied, find all the values, c, in the interval such that . If Rolle's Theorem cannot be applied, state why. 2.

  • Application of Rolle's Theorem for Closed Interval

    55693 Application of Rolle's Theorem for Closed Interval Please solve the problem to the specified answer and please provide as much explanation of each step as possible.

  • A Discussion On Rolle's Theorem

    all the conditions of Rolle's Theorem and g'(x)= f'(x) for all x what ever values of c in (a, b) satisfying f'(x)=0 will satisfy g'(x)=0 so, the interval here for which we can apply Rolle's theorem is [a, b] for part (b) g(x)=f(x-k) implies

  • Application of Rolle's Theorem

    Hence the solution A given problem is solved using Rolle's Theorem

  • Application of Rolle's Theorem

    Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's theorem can be applied, find all values of c in the open interval (a,b) such that f'(c) = 0.

  • Extrema and Rolle's theorem

    This solution shows how to locate and classify extrema of giving functions and use Rolle's theorem to formulate a proof about given continuous functions

  • Finding Critical Point Functions

    verify that the hypotheses of Rolle's Theorem are satisfied for each of the functions on the given intervals, and find the value of the number(s) "c" that Rolle's Theorem promises.

  • Rolle's theorem

    27931 Rolle's Theorem Please see attachments. Please see the attachment. This solution shows how to prove functions are continuous using Rolle's theorem.

  • Find the derivative

    Find the extrema of f on the given interval. f(x)=3x^2-10x+7; [-1,3] "Show that f satisfies the hypotheses of Rolle's Theorem on [a,b] and find all numbers c in (a,b) such that f'(c)=0."

View More Related Solutions