Question

How do you know what is the rate of change of the steepest section of an exponential graph?

Answer 1

Differentiate the exponential graphs equation- at the x point substitute the last value of the x that counts in the domain of the graph (that looks the steepest).

Answer 2

I'm not supposed to use differentiation - is there another way though? The picture I've attached is my exponential function that I'm talking about, with those domain restrictions.

Answer 3

Well rate of change refers to \(\dfrac{dy}{dx}\)...

Answer 4

Anyway can you draw the graph?

Answer 5

I know lol - but I'm taking advanced functions right now and we're not supposed to use that yet. We can use the different quotient and other things but not that

Answer 6

Alright.

Answer 7

It's the graph in black...

Answer 8

So there are no points to it?

Answer 9

Like on the x and y axis- no numbers?

Answer 10

No, we just use that equation, and from the equation and the graph, determine where the steepest point is

Answer 11

So you need the coordinates of that point?

Answer 12

Yeah, but my question is how do I get those coordinates/point?

Answer 13

Differentiate the exponential graphs equation- at the x point substitute the last value of the x that counts in the domain of the graph (that looks the steepest).
^You say this, so my last value of x is 28.3 (as mentioned in the restriction of the domain), so do I use this?

Answer 14

And after differentiating the exponential equation, and substitute 28.3, I find a value, but what is that value used for?

Answer 15

That's the gradient at that point- rate of change.

Answer 16

Ohh, so that's the value that I'm supposed to find then! Got it now, thank you!

Answer 17

No worries :)