Find the even extension of ` f(x) = {x^2-x^3,0 <= x < 34`

if f(x)={x^3+x^2,for0lt=xlt=2x+2,for2

if f(x)= {x^3+x^2,for 0lt=xlt=2x+2 ,for2

If f(x) ={{:(x^(3)+x^(2)quad "for" quad 0lexle2),(x+2 quad"for" quad 2ltxle4):} . Then find the even and odd extension of f(x)

Let the function f(x)=3x^(2)-4x+8log(1+|x|) be defined on the interval [0,1]. The even extension of f(x) to the interval [0,1]. The even extension of f(x) to the interval [-1,1] is

Find the derivative of f(x) =2x^(2)+3x-4 at x=0.

Find the derivative of the function f(x)=2x^2+3x-5 at x = 1 . Also prove that f^(prime)(0)+3f^(prime)(-1)=0 .

Find the derivative of f(x)=2x^2+3x-5 at x=-1 . Also, prove that f'(0)+3f'(-1)=0.

Let the function f(x)=4 sinx+3 cos x+ log (|x|+sqrt(1+x^(2))) be defined on the interval [0,1]. The odd extension of f(x) to the inteval [-1,1] is

Find the derivative of f(x) = 3 at x = 0 and at x = 3 .

If f:[-4,0]->R is defined by f(x) = e^x + sin x, its even extension to [-4, 4] is given by :