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

Consider f(x)={(4x+3,1lexle2),(3x+5,2lexle4):} Evaluate int_1^4f(x)dx

Let f(x)={{:(x^(2)",","for ",xle1),(1",","for ",1ltxle3),(5-2x",","for ",xgt3):} Then f'(6) is equal to

Let f(x)={{:(1-5x",","if ",xlt-2),(x^(2)-2x",","if ",-2lexle1),(-1+2x",","if ",xgt1):} Then the value of f(-1) is equal to

Consider f(x)={(4x+3,1lexle2),(3x+5,2lexle4):} Evaluate int_1^2f(x)dx and int_2^4f(x)dx

If f(X)={{:(x^2sin""(pix)/(2),|x|lt1),(x|x|,|x|ge1):} then f(x) is a)an even function b)an odd function c)a periodic function d)None of these

If f'(x)=x^3-2/x^2 and f(2)=3 find f(x)

Discuss the extremum of f(x) = 2x^(3) - 3x^(2) - 12x + 5 for x in [-2, 4] and find the range of f(x) for the given interval.