how do you find the gradient of a curve?

You must find the first derivative of your function, and then enter the x-value into it

first derivative:

d(8√x +x)/dx =

8d(√x)/dx + d(x)/dx =

8d(x^(1/2))/dx + 1 =

8∙1/2∙x^(-1/2)d(x)/dx + 1 =

4/√x + 1

now enter x:

4/√9 + 1 =

4/3 + 1 =

7/3

Differentiating a curve will give you the slope of the curve at any point (x,y) along the curve.

dy/dx = 4/√x + 1

Slope at x = 9 = 4/3 + 1 = 7/3

yes differentiate

y =8(x)^(1/2) + x

dy/dx = 8(1/2)x(-1/2) +1 = (4 /√x ) + 1

At x = 9

dy/dx = 4/3 + 1 = 2+1/3