If we assume a polynomial-like function, then we know that it will look kind of like a quartic.
It is concave up on both ends, and has a bump in the middle where it is concave down.
It has minima at x = -5 and x=3, and a maximum at x = -2
Since f"(x) = (x+3)(x-1) = x^2+2x-3
f'(x) = 1/12 x^4 + 1/3 x^3 - 3/2 x^2 + cx + d
I guess you can figure out what c and d are, but the graph will look kind of like
http://www.wolframalpha.com/input/?i=3x%5E4+%2B+16x%5E3+-+66x%5E2+-+360x+for+-6+%3C%3Dx+%3C%3D+5
Sketch the graph of a function having the following features:
f'(x)>0 on (-5,-2) and on (3,oo)
f'(x)<0 on (-oo,-5) and on (-2,3)
f''(x)>0 on (-oo,-3) and on (1,oo)
f''(x)<0 on (-3,1)
Please help!
1 answer