The graph of the derivative F^{\prime}(x) of some function F is given in the figure above. If F(20) = -270, estimate the maximum value attained by F on the interval [0,60].

Question

anonymous · Answer

where is the graph?

anonymous · Answer

attachment

anonymous · Answer

sorry my computer was bogging down

anonymous · Answer

no problemo. so, F'(50)=0 and there is either a maxima or a minima at x=50.

anonymous · Answer

ok that makes sense

anonymous · Answer

wouldnt it be the area under the F'(x) from x=20 to x=50 and add -270 to it?

anonymous · Answer

approximating it to a triangle, $$A=0.5*30*20=300\
F_{max}=300-270=30$$

anonymous · Answer

yeah that's it but I'm just looking at how you got that, not quite sure I follow

anonymous · Answer

as long as F' is +ve, the function F in increasing. So, we know the function increases from x=0 to 50. So, the maximum will be at x=50. Now, they have provided us with the value of F at x=20. So, all we need to find is by how much F increases from x=20 to 50. Which is what the area under the differential provides us with. That part of the curve is almost linear and can be approximated to a triangle. Do you follow?

anonymous · Answer

yes I do, the area that you find from 20-50 is added to the given value which is the area from 0-20 which is the part that took me a second.  I was able to do another one exactly like it so I'm pretty sure I've got it
Thanks!