Question

Sketch a possible graph of a function f that satisfies the following conditions:

(i) f(0) =0, f(2) = 3, f(4) =6, f'(0) =f'(4) =0

(ii) f'(x) >0 for 0<x<4, f'(x) <0 for x<0 and for x>4

(iii) f"(x) >0 for x<2, f"(x) <0 for x>2

Answer 1

(i)

f(0) =0, f(2) = 3, f(4) =6, f'(0) =f'(4) =0

(ii)

f'(x) >0 for 0<x<4, f'(x) <0 for x<0 and for x>4

(iii)

f"(x) >0 for x<2, f"(x) <0 for x>2