Determine when the function f(x)=3x^3+4x^2-59x-13 is less than 7

Answer 1

let's see when it IS 7

3x^3 + 4x^2 - 59x - 13 = 7
3x^3 + 4x^2 - 59x - 20 = 0

let's hope this factors nicely,
tried: x = ±1, ±2, ±4, yup worked for x = 4
did synthetic division ...
3x^3 + 4x^2 - 59x - 20 = 0
(x-4)(3x^2 + 16x + 5)
(x-4)(x+5)(3x + 1) = 0
x = 4, x + -5, x + -1/3

since this is standard cubic opening upwards, my rough sketch shows that it is < 7 for
x < -5 or -1/3 < x < 4

Answer 2

thankyou