identify the open intervals where the function f(x)=-5x^2+x+4 is increasing and/or decreasing

Question

anonymous · Answer

Do you have calculus knowledge? Differentiation in particular.

anonymous · Answer

yes

anonymous · Answer

Cool :) So we will use that. 
1st step get the derivative of the function. Go :)

anonymous · Answer

1-10x

anonymous · Answer

Cool, now make it equal to 0 and solve the equation

anonymous · Answer

ok i got 1/10

anonymous · Answer

Nice, do you know what happens at x=1/10 with this function?

anonymous · Answer

Where the derivative is =0

anonymous · Answer

it decreases?

anonymous · Answer

Nope, the derivative of a function is nearly the same as the rate of change. 
So when the derivative is 0, the rate of change of the function is 0. 
It is neither decreasing nor increasing.

anonymous · Answer

ok so would the answer be infinity?

anonymous · Answer

No. But we have found the point where it changes behavior. 
f(x)=-5x^2+x+4
This is an upside down parabola. So in this interval it is increasing 
$$(-\infty,1/10)$$
and 
$$(1/10 , \infty)$$
it is decreasing.

anonymous · Answer

ok thank you so much!