## anonymous one year ago When F is defined for x ≥ −6 by F(x)= integral from -6 to x (6t^2+5t-1)/(3+4t^2) dt. determine the largest interval(s) on which F is decreasing.

1. anonymous

2. freckles

have you found F'(x)?

3. anonymous

no, going to do it now

4. anonymous

F'(x)= (6x^2+5x-1)/(3+4x^2)

5. anonymous

@freckles so how do I find where F(x) is increasing?

6. freckles

the function F is increasing when F' is positive

7. freckles

the function F is decreasing when F' is negative

8. freckles

solve the inequality $\frac{6x^2+5x-1}{3+4x^2} <0$

9. anonymous

got it, thank you