uk.ixl.com has been visited by 100K+ users in the past month
KS3-aligned maths practice website. Comprehensive and Fun. Get ready!
This program is so fun! My kids love it. - Erin Slocum
Search results
- For a quadratic function ax2 +bx + c, we can determine the concavity by finding the second derivative. f (x) = ax2 + bx +c f '(x) = 2ax +b f ''(x) = 2a In any function, if the second derivative is positive, the function is concave up. If the second derivative is negative, the function is concave down.
socratic.org/questions/how-do-you-determine-the-concavity-of-a-quadratic-function
People also ask
How do you determine the concavity of a quadratic function?
How do you know if a function is concave?
How do you find the concavity of f(x)?
How do you find the concavity of a function?
Can a second derivative determine concavity without a graph?
How do you know if a graph is concave?
Review your knowledge of concavity of functions and how we use differential calculus to analyze it.
- You have two functions f and g, where f''>0 and g''>0. If you take the second derivative of f+g, you get f''+g'', which is positive. So their sum i...
- In order for 𝑓(𝑥) to be concave up, in some interval, 𝑓 ''(𝑥) has to be greater than or equal to 0 (i.e. non-negative) for all 𝑥 in that inter...
- In general, no. Points where f"(x)= 0 are specifically called inflection points. But in the example provided, -2 is also a critical point (Observe...
- Product rule: d/dx[f(x)*g(x)] = f'(x)g(x) + f(x)g'(x) f(x) = (x-1)³ and g(x) = x
Sep 21, 2014 · For a quadratic function ax2 +bx + c, we can determine the concavity by finding the second derivative. f (x) = ax2 + bx +c. f '(x) = 2ax +b. f ''(x) = 2a. In any function, if the second derivative is positive, the function is concave up.
Aug 26, 2020 · Here is a proposed definition: A function f is said to be concave up on an interval [a, b] if for all x, y ∈ [a, b] with x <y, the line L connecting (x, f(x)) and (y, f(y)) satisfies L(t) ≥ f(t) for all t ∈ (x, y). It is concave down if the final inequality is reversed. Share. Improve this answer.
Fortunately, the second derivative can be used to determine the concavity of a function without a graph or the need to check every single x-value. It is for this reason that given some function f(x), assuming there are no graphs of f(x) or f'(x) available, the most effective way to determine the concavity of f(x) is to use its second derivative.
I am given a function $f(x)$. I determined that $f(x)'' = 0$ precisely when $x$ is $4$ or $-3$. I am asked to find the interval for which the function is concave down. How can I do it by knowing the values $x = 4$ and $x = -3$ and without having to plot the function?
Dec 21, 2020 · The canonical example of \(f''(x)=0\) without concavity changing is \(f(x)=x^4\). At \(x=0\), \(f''(x)=0\) but \(f\) is always concave up, as shown in Figure \(\PageIndex{11}\). Figure \(\PageIndex{11}\): A graph of \(f(x) = x^4\). Clearly \(f\) is always concave up, despite the fact that \(f''(x) = 0\) when \(x=0\).
Questions. How do you determine the concavity of a quadratic function? How do you find the concavity of a rational function? What is the concavity of a linear function? What x values is the function concave down if #f (x) = 15x^ (2/3) + 5x#? How do you know concavity inflection points, and local min/max for #f (x) = 2x^3 + 3x^2 - 432x#?
