Question

f(x)=x^3-5x^2+3x-7. Using calculus methods find points where the line tangent to the curve is horizontal. Please show work!

Answer 1

find the derivative. horizontal tangents occur when the derivative is equal to zero.
f'(x)=3x^2-10x+3
Setting equal to zero:
3x^2-10x+3=0
(3x-1)(x-3)=0
This is zero when either 3x-1=0 or x-3=0 so,
x=1/3 or x=3
Plug these x values into f(x) to get your points (1/3, f(1/3)) and (3, f(3)) where the tangent is horizontal.

Answer 2

wow that makes so much sense thanks so much

Answer 3

np :)