Maths Trial Questions!!! (1 Viewer)

[louielouiee]

Consider the function A= x/lnx

a) For what values of x is the function differentiable? 2 marks

b) Find the gradient of the tangent to the curve when x= θ^2 3 marks

c)Find where the gradient of a tangent to the curve is -1 3 marks

d) Find the coordinates of all stationary points and determine their nature 4 marks


The answer to any question would be helpful!

Enjoy

 

[louielouiee]

Anybody? No? Fine!

 

[asianese]

Consider the function A= x/lnx

a) For what values of x is the function differentiable? 2 marks

b) Find the gradient of the tangent to the curve when x= θ^2 3 marks

c)Find where the gradient of a tangent to the curve is -1 3 marks

d) Find the coordinates of all stationary points and determine their nature 4 marks


The answer to any question would be helpful!

Enjoy

a) Differentiable when lnx =/= 0 ie when x>0
b)

I have no idea why my latex is stuffing up.

b) Differentiate using the quotient rule and then substitute
c) Solve for when the derivative = -1
d) Let the derivative = 0 and solve for all solutions of x
Find the second derivative and substitute those x values. A'' > 0 concave up, relative min, A'' <0 concave down, relative max
Or use a first derivative table and substitute values near those x values.
Substitute those x values into A and then find the coordinates of your stationary points.

 

[D94]

I have no idea why my latex is stuffing up.

ftfy...

Add \\ for new lines (but don't hit 'enter') and you don't need to put \ in front of

 

[louielouiee]

Thanks, that makes it easier for me!

 

[Drongoski]

a) Differentiable when lnx =/= 0 ie when x>0

x>0 and x=/= 1 (ln 1 = 0).

 

[Carrotsticks]

you don't need to put \ in front of

You don't NEED to, but it looks nicer.

With \ in front:



Without \ in front:



Similarly:

 

[asianese]

Of course it looks nicer =)