Wednesday
May 4, 2016

# Homework Help: Calculus

Posted by Dan on Monday, November 29, 2010 at 9:53pm.

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
• Calculus - Reiny, Monday, November 29, 2010 at 10:14pm

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 + .....

• Calculus - Dan, Tuesday, November 30, 2010 at 8:55am

i still did not understand. if u dont 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 :).