Convexitya Consider the function f(x) : R +R where pe R is a scalar:f(x) = |x|P.Show that, when p > 1, f(x) is convex. Show that, when 0 < p<1, f(x)is neither convex nor concave. Further, show that, when 0 0.

in the given question we have to check the concave and convex function but before check we know…

3 Convexity a Consider the function f(x) : R→ R where p e R is a scalar: S(x) = |x|". Show that, when p 2 1, f(x) is convex. Show that, when 0 < p < 1, f(x) is neither convex nor concave. Further, show that, when 0 < p< 1, f(x) is concave on the interval (-0,0] and is also concave on the interval [0, 0). b Let S be a nonempty, convex set in R". A function f(x) : S¬R is called quasi-convex if, for all 2 e [0, 1] and x1, x2 E S: f (Ax1 + (1– a )x2) s max [f(x1), f(x2)]. Show that a convex function is also quasi-convex. Using an example, show that a quasi-convex function is not necessarily convex. Hint Try the function in Part a.

3 Convexity a Consider the function f(x) : R→ R where p e R is a scalar: S(x) = |x|". Show that, when p 2 1, f(x) is convex. Show that, when 0 < p < 1, f(x) is neither convex nor concave. Further, show that, when 0 < p< 1, f(x) is concave on the interval (-0,0] and is also concave on the interval [0, 0). b Let S be a nonempty, convex set in R". A function f(x) : S¬R is called quasi-convex if, for all 2 e [0, 1] and x1, x2 E S: f (Ax1 + (1– a )x2) s max [f(x1), f(x2)]. Show that a convex function is also quasi-convex. Using an example, show that a quasi-convex function is not necessarily convex. Hint Try the function in Part a.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Given the function,Show that it is not continuous at (3,-1) and determine the slope of the line tangent to the trace of the graph of f on the plane y=-1 at the point (3,-1,0).
[-/3.44 Points] DETAILS MY NOTES LARCALC12 13.3.130. Consider the function f(x, y) = (+5 +y₁ ·45) 1/5 (a) Find fx (0, 0) and f₁(0, 0). fx(0, 0) fy(0, 0) = = (b) Determine the points (if any) at which fò(x, y) or fy(x, y) fails to exist. (If there is no answer, enter NONE.) fx(x, y) and fy(x, y) fail to exist for y = , X % 0.
A function F is defined on R² By: f (x, y) (x, y)# (0,0) F (x, y) = (x, y) = (0,0) y+2xy² x²+y2 Let f (x, y) se that is, F1(x, y)and F2 (x, y) when (x, y)÷(0,0). ду -find and
Consider a function z = F(u(s, t), v(s, t)) where F, u, and u are differentiable and u(8, 6) = -1, v(8, 6) = 2, u, (8, 6) = 5, u, (8, 6) = 9, vs(8, 6) = −3, v₁(8, 6) = 4, Fu(-1,2) = -4, and F(-1,2)= -10. Compute and when s = 8 and t = 6 dt
Q3) State the approximation for a differentiable function f(x): (a) V51 (b) V123 (c) (33)
EMERGENCY
ضحفهطضتبةؤةئرردضجق
Could you please do all parts and provide written solutions , with explanations
can i get help with this function
A function f:R →R, where R'is the set of all real number satisfies the equati on. **- Ax) + f(v)+f(0) 3. for all x,y e R If f(x) is differenti ability at x = 0,then show that f'(x) exist for all x e R. 11