stationary points help! (1 Viewer)

[lolzlolz]

can someone help me with Q13 please

 

[lolzlolz]

can someone help me with Q13 please

 

[ExtremelyBoredUser]

can someone help me with Q13 please

take the derivative

dy/dx = 3x^2 - 2ax + b (is the derivative of y )

and now at x = -1, 2 the gradient is 0 at is a stationary point (remember that the derivative can be considered as the gradient to y).

hence

dy/dx = 0;

3(-1)^2 - 2a(-1) + b = 0
3(2)^2 - 2a(2) + b = 0

Now you get a pair of simultaneous equations

2a + b = - 3 : Equation (1)
4a - b = 12 : Equation (2)

Using elimination method for these equations:

2a + b = - 3
4a - b = 12
-------------------
6a =9
a = 3/2 = 1.5

and from eqn 2,

b = 4a - 12
b = 4(1.5) - 12 = -6

Just did this mentally so double check for errors.

Edit: originally solved equation for x = -1, 3 as stat points.

 

[lolzlolz]

take the derivative

dy/dx = 3x^2 - 2ax + b (is the derivative of y )

and now at x = 1, -3 the gradient is 0 at is a stationary point (remember that the derivative can be considered as the gradient to y).

hence

dy/dx = 0;

3(1)^2 - 2a(1) + b = 0
3(-3)^2 - 2a(-3) + b = 0

Now you get a pair of simultaneous equations

2a - b = 3 : Equation (1)
-6a - b = 27 : Equation (2)

Using elimination method for these equations:

6a - 3b = 9 (multiplying (1) by 3)
-6a - b = 27 (keeping (2) the same)
----------
0a - 4b = 36 (adding both equations together)

b = -36/4 = -9

from rearranging equation (1), 2a - b = 3 therefore 2a = 3 + b

2a = 3 + b
= 3 - 9
2a = - 6

hence a = -3

so a = -3, b = -9.

Just did this mentally so double check for errors.

solutions say a is 1.5 and b is -6

 

[ExtremelyBoredUser]

solutions say a is 1.5 and b is -6

LOL NO hold on i misread, its x=2 and x =-1 for stat points, oops. I'll quickly edit the sols haha oops

 

[ExtremelyBoredUser]

solutions say a is 1.5 and b is -6

The same process anyways, I updated my original post now, should be straightfroward.

at x = a,b there is stat points. stat points are gradient = 0 so find the derivative and substitute the respective x coordinates into the derivative function then make that equal to 0. You should get 2 simultaneous equations and then rest is just algebra.