Question

Find:
(a) the interval(s) on which f is increasing,
(b) the interval(s) on which f is decreasing,
(c) the open interval(s) on which f is concave up,
(d) the open interval(s) on which f is concave down, and
(e) the X-coordinate(s) of any/all inflection point(s).

f(x)= (x^4) - (4802 x^2) + 9604

Answer 1

take the first derivative ....
a) f is increasing for all values of x for which f '(x) is positive
f is decreasing for all values of x for which f '(x) is negative

take the second derivative
c) if the second derivative is positive, f is concave up
d) if the second derivative is negative, f is concave down
e) set the second derivative equal to zero and solve for x

f '(x) = 4x^3 - 9604x
= 4x(x^2 - 2401)
= 4x(x-49)(x+49)

What conclusions can you draw from that?
Use what you know about the properties and general shape of y = x^4 + .....

Answer 2

i still did not understand. if u don't mind could you please explain it again and also the question asks for the intervals and the points. could you give the intervals and points for the the questions above in the questions .. Thanks a bunch :).