find the points on a graph of f where the tangent line is horizontal.

Question

f(x)= x^3 - 18x^2

(x,y)= (smaller x value)
(x,y)= (larger x value)

Answer 1

For the given curve:
f(x)= x^3 - 18 x^2

The tangental gradient is the derivative:
f'(x)= [d/dx](x^3 - 18 x^2)

The tangent is horizontal when its gradient is 0.

0 = f'(x)

Find the roots. (Hint: Factorise)