Posted by **andy** on Thursday, July 18, 2013 at 12:40pm.

How many integer values of a are there such that

f(x)=x^+ax^2+8ax+25

has no local extrema?

- calculus -
**Steve**, Thursday, July 18, 2013 at 1:10pm
Assuming you meant

x^3+ax^2+8ax+25

we want a derivative with no zeros. So,

f' = 3x^2 + 2ax + 8a

f" = 6x+2a

this will have no zeros if the discriminant is negative, so we need

(2a)^2 - 4(3)(8a) < 0

4a^2 - 96a < 0

4a(a-24) < 0

So 0<a<24

At a=0 and a=24, f"(0) when f'=0, so there's an inflection point, so no extrema.

So, 0 <= a <= 24

## Answer This Question

## Related Questions

- Calculus - PLEASE HELP!! - For any real number x there is a unique integer n ...
- math - Given the function f(x)=x^4−6x^2 a.) Find all values of x where ...
- Calculus - find the intervals on which f(x) is increasing and decreasing along ...
- Calculus; Limits - Evaluate limit, x -> a, [(x + 4a)^2 - 25a^2] / [x - a] My ...
- Calculus - let f(x)=x^3(e^-x) Answer using calculus, use graphing calculator ...
- Calculus - Find the x-values of all points where the function below has any ...
- Math - How many x-intercepts and how many local extrema does the polynomial P(x...
- Calculus - For any constant c, define the function f_c(x)= x^3+2x^2+cx. (a) ...
- Calculus - For any constant c, define the function f_c(x)= x^3+2x^2+cx. (a) ...
- Calculus - For p = 15e^-x, 0 < x < 7, find the local extrema

More Related Questions