Question

The graph of f(x)= 2x³ + 12x² - 126x +24 has two horizontal tangents.

What is the negative value of x where a horizontal tangent occurs?
What is the positive value of x where a horizontal tangent occurs?

Answer 1

Hi,
the negative value of x where a horizontal tangent occurs is -7

the positive value of x where a horizontal tangent occurs is 3

Explanation:

`f(x)=y=2x^3+12x^2-126x+24\\\\y'=6x^2+24x-126=6(x^2+4x-21)\\\\y'=0 \Longleftrightarrow\ x=3\ or\ x=-7\\\\since\ \Delta=16+4*21=100=10^2\\\\x=(-4+10)/(2) \ or\ x=(-4-10)/(2)`