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Prove if $f$ is a concave function, then $f (\frac{a x_{1} + b x_{2} + c x_{3}}{a + b + c}) \geq \frac{a f (x_{1}) + b f (x_{2}) + c f (x_{3})}{a + b + c} .$

Goundoubuf 2022-11-25

Use the Fundamental Theorem of Calculus to calculate the definite integral. Give an exact answer
$\int_{0}^{\frac{π}{2}} e^{\cos θ} \sin θ d θ$

Lorena Becker 2022-11-25

Find the derivative of $s e c x$ .

Jay Park 2022-11-25

Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.)
$lim_{t \to 2} \frac{(t^{4} - 3)}{(2 t^{2} - 3 t + 7)}$

blogmarxisteFAu 2022-11-25

Integral $\cos (2 θ)$ ?

Scarlet Marshall 2022-11-25

What is the Derivative of $y = \sec^{2} (x)$ ?

nonhumanWd3 2022-11-25

Knowing that: $\int e^{k x} d x = \frac{1}{k} e^{k x} + c$ show that $\int a^{x} d x = \frac{1}{\ln a} \cdot a^{x} + c$

Marques Flynn 2022-11-25

Mean value for a concave function over $[0, 1]$ VS $f (1 / 2)$

Neil Sharp 2022-11-25

Given a concave function $f (x)$ , why $f (x) - x f^{'} (x) > 0$ ?

liachta6VW 2022-11-25

Find the derivative of a function $\frac{\ln x}{x}$ .

valahanyHcm 2022-11-24

Is this function increasing/decreasing and convex/concave?
$y = 3 x + \ln (\frac{3 x - 4}{x - 1})$

Jamie Medina 2022-11-24

Use a double integral to find the volume of the indicated solid. $z = 1 - x y, y = x, y = 1$

merodavandOU 2022-11-24

Find f such that f'(x)=8x-7, f(9)=0
f(x)=

ingerentayQL 2022-11-24

Let C be the curve of intersection of the parabolic cylinder $x^{2} = 2 y$ , and the surface $3 z = x y$ . Find the exact length of C from the origin to the point (2, 2, 4/3).

Jazlyn Nash 2022-11-24

Suppose $γ \in R^{1}$ and $β \in R^{k}$ .
Let $f (γ, β) = (y_{2} - γ y_{1}) - (y_{3} - γ y_{2}) \exp (x^{'} β)$
Then is f a concave function of $(γ, β^{'})$ ?

gheadarce 2022-11-24

Find the derivative of the function
$y = \ln (\frac{x}{x + 5})$
$y^{'} = ?$

Jamie Medina 2022-11-24

Given a function $f (x)$ on $R$ , and that $f (x)$ is strictly increasing and strictly concave: $f^{'} (x) > 0$ , and $f^{″} (x) < 0$ . Is it always true that, for such function, we have:
$f (a + b) < f (a) + f (b)$
$a, b$ are real numbers.

Scarlet Marshall 2022-11-24

Evaluate the line integral, where C is the given curve.
$\int_{C} x y d s, C : x = t^{2}, y = 2 t, 0 \leq t \leq 3$
thanks show all work and steps

neudateaLp 2022-11-24

the equation f(x)′−f(x)=0 holds for the exponential function on the complex plane.Now what i dont understand is this.
"let $f (x) = a_{0} + a_{1} X + a_{2} X^{2} . . . . . . . .$ f is a polynomial with infinite degree ".Why is that. I dont understand how he came to that conclusion?I mean Why define it that way?.MAybe he could solve the ODE on the real numbers and avoid this "out of nowhere" polynomial or is there a connection?

neimanjaLrq 2022-11-24

Positive constant divided by a concave function, how to convexify this constraint?

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