Question

Working on this for a long time. State the subintervals of (-5, 4) on which the derivative of F is positive. Please see the the attached

Answer 1

So the derivative being positive simply means that the slope at those points is positive. So look for where the slope is positive. (-5,-4) and (3,4)

Answer 2

I see thank you

Answer 3

Positive derivative means that graphically the tangent to the curve at a point has positive gradient - or is upwards going to the right as traditionally plotted. That appears to be (-5,-4) - not including at x = 4 as the 'pointiness' of the function there implies that F does not have a derivative defined at that point. The limiting value of the gradient quotient must not only exist, but be equal either side of some point being tested. The other interval appears to be [3,4] - including the endpoints here.

Answer 4

I've also excluded x = -5 as it's not clear from the problem whether the function is defined AT x = -5.