SOLUTION: Hi, i'm not sure which topic it should go in but anyway... i am struggling to find out how to get the answer to this. 'Find the gradient of the following curves at the given

Question 159386This question is from textbook pure core maths1 & 2
: Hi, i'm not sure which topic it should go in but anyway...
i am struggling to find out how to get the answer to this.
'Find the gradient of the following curves at the given point'
y = 3*rootx(x-2)^2
at the point where x = 3
i have got the equation to
y = 3*rootx(x^2 -4x + 4)
i then have to find the gradient (dy/dx) and substitute in x (3)
but i can't get the right answer, which the book says is 29*root3
thanks in advance. This question is from textbook pure core maths1 & 2

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
First off, let's do a substitution.
Let

then

Now we can go back and substitute,
Let's look at u,

Substitute all those values into dy/dx,

Is this the answer you got??
.
.
.
We can check the answer by calculating dy/dx near 3 using x and y values.
Let's use
x=2.99, then
x=3.00, then
x=3.01, then
then we can calculate the derivative on the left of 3 and the right of 3 and take the average.
(dy/dx)left=y(3.00)-y(2.99))/(3.00-2.99)=(5.196152-5.13561)/(0.01)=6.054233
(dy/dx)right=y(3.01)-y(3.00))/(3.01-3.00)=(5.256854-5.196152)/(0.01)=6.07011
We take the average of those two and get
(dy/dx)(3)=6.062
Let's look at the value we calculated,

Looks like the two match.
.
.
.
Meanwhile, the answer you provided doesn't look close.
is not near the answer we calculated and verified.
Check the answer again.
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