Any function is said to have a maximum if :?

Question

(a) d^2y/dx^2 < 0
(b) dy/dx < 0
(c) d^2y/dx^2 > 0
(d) d^2y/dx^2 = 0

Answer 1

any function f(x) is said to have a local "maximum" if the second derivative at that point is less than zero (i.e, negative), hence (A) is the correct answer. The opposite is true, namely if the second derivative at the point in question is positive (above zero), it will be a local minimum. lol, haven't even thought about maths since university!

Answer 2

choice (a) d2y/dy^2<0

Answer 3

none, not even local maximum
counterexamples:
a) y=ln x on (0,infinity)
b) y = -x on R
c) y=e^x on R
d) y = x on R
not even combinations of two

Answer 4

c