Question

find the values of x for which the curve has horizontal tangents

Answer 1

N 7

we have

$y=x^3-2x^2+x+1$

step 1

Find out the first derivative

$y^{\prime}=3x^2-4x+1$

step 2

Equate the first derivative to zero

$3x^2-4x+1=0$

Solve the quadratic function

the solutions are

x=1/3 and x=1