differentiation

Question

 

b) For the curve 𝑦=𝑥𝑒^−𝑥^2 ,𝑥 ≥0

i. Find the coordinates of the point where the gradient is 0 giving your answers exactly.

ii. Show that the line 𝑦=𝑥 is a tangent to the curve 𝑦=𝑥𝑒−𝑥2 and give the coordinates of intersection between the line and the curve.

iii. Find the 𝑥 coordinate of the point where the gradient of the curve is a minimum giving your answers exactly.

iv. Write down the coordinates of the curve where the gradient is a maximum.

 

For part iii. I was wondering how I would do this when 𝑥≥0 would the x coordinate simply be 0??

 

Thanks.

Answer 1

You are missing part of your function.

Specifically, what is the exponential function e^x or e^y ?

THEN when you state the function a second time, you have just e.

What exactly is the function?

 

If it is e^x then the derivative is not zero anywhere.

If it is e^y then you must do implicit differentiation.

 

BTw you can graph functions at www.desmos.com