Find the relative maxima and relative minima, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = x3 − 48x + 4 relative maximum (x, y) = relative minimum (x, y) =

Answer 1

x^3 - 48x + 4

take the derivative and set it equal to zero

3x^2 -48 = 0

x^2 = 48/3 = 16

x = sqr16 = + or - 4

at x=+4, y = (4)^3 -48(4) + 4 = 64 -192+4 = -124

the point (4,-124) is a local or relative minimum

at x-4 y=(-4)^3 -48(-4)+4 = -64 + 192 + 4 = 122

the point (-4, 22) is a local or relative maximum