A level maths help

How would you find the gradient of an inverse function. we never learned how to do this and the mark scheme is confusing. (Question below)

(part c)

Reply 1

subbhy

Original post by firestudent

How would you find the gradient of an inverse function. we never learned how to do this and the mark scheme is confusing. (Question below)

(part c)

I think you would need to find the equation of the inverse function.

Use that to determine the x coordinate given y=3

Differentiate it to obtain the gradient function. Calculate the gradient at the x value that corresponds to the y value of 3

Reply 2

firestudent

Original post by subbhy

I think you would need to find the equation of the inverse function.
Use that to determine the x coordinate given y=3
Differentiate it to obtain the gradient function. Calculate the gradient at the x value that corresponds to the y value of 3

Ok that sounds like it would work. Here is the mark scheme method Screenshot 2024-06-16 101812.png

I'm not entirely sure what they've done

Reply 3

subbhy

Original post by firestudent

Ok that sounds like it would work. Here is the mark scheme method Screenshot 2024-06-16 101812.png

I'm not entirely sure what they've done

I think they’ve done what I said

Reply 4

davros

Original post by firestudent

Ok that sounds like it would work. Here is the mark scheme method Screenshot 2024-06-16 101812.png

I'm not entirely sure what they've done

Looks like they've worked out h'(3) and then used the fact that the gradient of the inverse function at y = 3 is the reciprocal of the original function at x = 3.