Question

For y = x^4 - 72x^2 - 17, how would I find each of these? a) where the function is increasing b) where the function is decreasing c) where the function is concave up d) where the function is concave down e) inflection points

Answer 1

For the answer to the question above,
a) dy/dx = 4x^3 - 144x. When is this > 0? When x^3 > 36x.
b) When is dy/dx < 0? When x^3 < 36x
c) 2nd derivative = 12x^2 - 144. Concave up when 2nd derivative is positive
d) Concave down when 2nd derivative is negative
e) dy/dx = 0 when x = 0, -6, +6
f ) 2nd derivative = 0 when 12x^2 - 144 = 0, x = -sqrt(12) and +sqrt(12)