Thread: Help with derivative of graphs please

Can someone help me find the derivative of graphs F,G,H and why they are the derivative please?

(Picture of Question attached in two files below)

Thanks

1. c) is the derivative of a)
2. f) is the derivative of d)
3. b) is the derivitive of h)

and g) and e) are irrelevant

Assuming u know:When the derivative function = 0 at a point x, then y at x is a turning point (trough or a crest)

first one because the turning points of a), (ie when gradient is 0), at at the x-intersections of c). This is the same for second one.

How ever you might think that e) is the derivative of c):
-the thing is that y value e) goes from negative to positive in the first intersection (from left)
-and the first (from left) turning point is a crest, which goes from positive and negative gradient
- so e) is not the derivative of c)

If you integrate c) you get a power-4 graph, and we've used the only one
If you differentiate it, you get a straight line: which there is none

So we are left with b), g) and h):
Personally, Ive never seen a graph like h) before.
But this is what i think:

lets divide the graph curves into positive x (right) and negative x (left)

consider b) having a derivative
left: the gradient is positive
right: the gradient is positive
both other graphs have curves negative y, so b) doesnot have a derivative.

Consider g)
left:gradient is negative
right: gradient is positive
y values of h) are always negative and b) is positive on the left and negative on the right (opposite)
So g) also does not have a derivative

So h) does have one
gradient
-left: positive
-right:negative
-also when x approaches 0, the gradient is infinitely negative/positive

And these properties are shown in the curve b), and so... the third pair.

Now Ive said a bit tooo much