Mathematics - Stuck on a question

Hi Mature student here.

Find the gradient of the curve with the equation y = 3(sqrt(x)) at point where:
a: x = 4

WORKINGS SO FAR

let x = 4, therefore y = 3 * 2 = 6 (sqrt(4) = 2)

I define this P

I then choose another point to the right of the x = 4 location

let x = 16, therefore y = 3 * 4 = 12 (sqrt(16) =4)

I define this as Q

Q co ordinates are (16, 12) which are also (x2, y2)
P co ordinates are (4, 6) which are also x1, y1)

Use formula (y2 - y1) / (x2 - x1) to find m (gradient)

12 - 6 = 6 and 16 - 4 = 12, therefore 6 / 12 = 0.5

THE ANSWER PAGE IS SAYING 0.75. What am I doing wrong.

(edited 1 month ago)

Reply 1

kjhhowell

Ok I think I got it...

I was having a brain malfunction...

So what I had to do was take the derivative of y = 3 sqrt(x) WHICH gives the >>>GRADIENT<<<

Which would have been f '(x) = 3/2(x)^(-(1/2)) or 3/2(x)^1 half

I then substitute x = 4 and hey presto we have 3/4

RaWR.

Reply 2

Yipiyap_EthanP

Official Rep

Original post by kjhhowell

Ok I think I got it...
I was having a brain malfunction...
So what I had to do was take the derivative of y = 3 sqrt(x) WHICH gives the >>>GRADIENT<<<
Which would have been f '(x) = 3/2(x)^(-(1/2)) or 3/2(x)^1 half
I then substitute x = 4 and hey presto we have 3/4
RaWR.

Well done for getting there yourself.

You can always use the power of 1/2 as a square root when doing differentiation and integration!