CAL HW PLEASE HELP

Question

Find a function f such that f ′(x) = 3x³ and the line 24x + y = 0 is tangent to the graph of f.

f(x) = 

 

Answer 1

f(x) = the integral of f'(x) = (3/4)x^4 + c (c is an unknown constant)

f'(x) =3x^3 = -24 = slope (y=-24x) the coefficient of the x term in the tangent line

x^3 = -24/3 = -8

x = -2 the cube root of -8

y= -24(-2) = 48

f(-2) = (3/4)(-2)^4 + c = 12+c = 48

c = 36

f(x) = (3/4)x^4 + 36