Differentiation help AS exam bank q11

How do you do f(x) = 8x²- 80/3 x^3/2 + 5x; x> 0
Find the x-coordinates of the points on the curve with equation y = f(x) where the gradient is equal to -4.

Reply 1

babushka22

At which point exactly are you stuck on this question - could you post your workings so far?

Reply 2

davros

Original post by MyNameIsName77

How do you do f(x) = 8x²- 80/3 x^3/2 + 5x; x> 0
Find the x-coordinates of the points on the curve with equation y = f(x) where the gradient is equal to -4.

differentiate, set the gradient function equal to -4, and solve the resulting equation.

Post your working if stuck :smile:

Reply 3

davros

Original post by agathaharkness

Hey,
1) differentiate the equation of the curve
f’(x)= 16x-40x^1/2+5
2) as we know that the derivative is the gradient we can say that
16x-40x^1/2+5=-4
3) this forms an equation which is a disguised quadratic
So when x=z^2
16z^2-40z+5=-4
16z^2-40z+9=0
4) factorise to find z
(4z-1)(4z-9)=0
z=1/4
z=9/4
5) find x
X=z^2
So
x= 1/16
x=81/16
Hope this helps. Sorry if I made any mistakes with the working, the ideas behind answering this question will hopefully help regardless 🙂