Question

if d/dx f(x) = 4x³ - 3/x⁴. such that f(2) = 0 , then f(x) is;

Answer 1

HELLO DEAR,

GIVEN THAT:- f(2) = 0 , and df(x)/dx = 4x³ - 3/x⁴

now, d/dx f(x) = 4x³ - 3/x⁴

∴ anti derivative of (4x³ - 3/x⁴) = f(x)

f(x) = ∫(4x³ - 3/x⁴).dx

f(x) = ∫4x³.dx - ∫3/x⁴.dx

f(x) = 4∫x³.dx - 3∫x⁻⁴.dx

f(x) = 4x⁴/4 - 3(-x⁻³/3) + c

f(x) = x⁴ + 1/x³ + c

∴ also, f(2) = 0.

so, f(2) = (2)⁴ + 1/(2)³ + c = 0

0 = 16 + 1/8 + c


128 + 1 + 8c = 0​

8C = -129

C = -129/8

∴ f(x) = x⁴ + 1/x³ - 129/8.

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Answer:

Ans is

X⁴+(1/X³)-129/8