Concave Up Or Down Calculator Math

For f x 2 x3 6 x2 10 x 5 f is concave up from negative infinity to the inflection point at 1 1 then concave down from there to infinity.

Concave up or down calculator math. Parts of concave up curves can decrease at decreasing rates and parts of concave down curves can decrease at increasing rates. In general you can skip parentheses but be very careful. Differentiate using the power rule which states that d d x x n is n x n 1 where n 2. Concave up also called convex or concave down are descriptions for a graph or part of a graph.

The calculator will find the intervals of concavity and inflection points of the given function. Printable pages make math easy. The graphs of two quadratic functions are shown below. The graph is concave down because the second derivative is negative.

Find the open intervals where f is concave up c. Now set it equal to 0 and solve. To solve this problem start by finding the second derivative. We have seen previously that the sign of the derivative provides us with information about where a function and its graph is increasing decreasing or stationary we now look at the direction of bending of a graph i e.

Also be careful when you write fractions. In fact you shouldn t be satisfied either. Free math problem solver answers your algebra geometry trigonometry calculus and statistics homework questions with step by step explanations just like a math tutor. Whether the graph is concave up or concave down.

The derivative is f x 15x2 4x 3 using power rule the second derivative is f x 30x 4 using power rule and 30x 4 is negative up to x 4 30 2 15 and positive from there onwards. Since 1 is constant with respect to x the derivative of 1 with respect to x is 0. Find the points of inflection b. F x x 2 1 x d d x x 2 d d x 1 x 2 1 2.

If a is negative the graph of f will be concave down on the interval since f x 2 a is negative. That kind of information is useful when it comes to analyzing graphs using derivatives. Y 2 x 2 2 x 1 whose graph is convcave up because its leading coefficient a 2 is positive and y x 2 3 x 1 whose graph is convcave down because its leading coefficient a 1 is negative. The mathematicians aren t satisfied if we say that a curve is concave up if it is increasing at an increasing rate or concave down if it is increasing at a decreasing rate.

A concave up graph looks roughly like the letter u. Questions for each function a. E 3x is e 3 x and e 3x is e 3 x. A concave down graph is shaped like an upside down u.

Are you ready to be a mathmagician. In general you can skip the multiplication sign so 5 x is equivalent to 5 x. They tell us something about the shape of a graph or more specifically how it bends. What do concave up and concave down mean.

F x is concave downward up to x 2 15. A concave up graph has the u or bowl right side up. 1 x 2 ln x is 1 x 2 ln x and 1 x 2 ln x is 1 x 2 ln x. F x x 2 1 x 2 x d d x 1 x 2 1 2.