Let

Question

f(x) = x3 − 7x2.
Find the point(s) on the graph of f where the tangent line is horizontal.

(x, y) =

I already got the smaller value, but I'm not getting the larger value right

Answer 1

I think you meant to type
f(x) = x^3 - 7x^2

f '(x) = 3x^2 - 14x
= 0 when the tangent is horizontal

x(3x-14) = 0
x = 0 or x = 14/3

if x=0, f(0) = 0
if x=14/3 , f(13/4) = ... (you do the arithmetic)

Notice there will be two points.
You said "I already got the smaller value....."
I sense that you are quite confused here.
There is no case of larger or smaller value here, it is a case of either x or y (which is f(x) )