Question

Sketch a continuous curve y=f(x) with the following properties: f'(x)>0 for x<0; f'(x)<0 for x>0; f''(x)<0 for x<4. I am super bad at graphing, and would appreciate it some more if someone can explain :D

Answer 1

f'(x) > 0 for x<0 means it is increasing on -infinity to 0
f'(x)<0 for x>0 implies its decreasing for x>0
f''(x) <0 for x<4 implies its concave down for x<4

Answer 2

\(f(x) = -x^2\)
should do it

Answer 3

wait are you sure, because that graph isn't concave down for x<4

Answer 4

its concave down for all x

Answer 5

\(f''(x)=-2\)

Answer 6

alright, thanks!

Answer 7

wait my bad i forgot to put f(2)=3

Answer 8

\(f(x) = -x^2+7\)