Question

Draw a function of dy/dx for the graphical below (image). Please help!

Answer 1

Step-by-step explanation:

Remember that

$\frac{dy}{dx}$

is the gradient or slope function.

So we need to analyze the slope of each graph over given time.l and how it changes.

For the 1st graph, we have a linear function.

Remember the special properties for all linear functions:

The slope at any two points on the line is the same.

So this means our slope here must be constant.

And since our slope is negative, our dy/dx, function must be a constant function that is negative. So

The answer for the first graph is draw a horizontal line underneath the x axis.

For the 2nd graph, we have a slope that is decreasing, reaches 0 at the minimum, then increases even more.

We can draw a linear function that is increasing forever for our dy/dx.

For the 3rd graph, we are increasing , till we hit 0, then decrease until we hit 0, then forever increases.

Our dy/dx will be a parabola that passes through the x axis twice at two different points, facing upwards.

The first , second, and third graph is the dy/dx graphs shown respectively.

All these are examples of possible graphs. If you need more clarification, let me know