Question

22.If-f(x) = 4x3-4such that f(2) 0. Then f(x) isdx1 129(A) 4+-129441291 1294

Answer 1

The function is given as,

d dx f( x )=4 x 3 − 3 x 4

We have to calculate the integral of ∫ d dx f( x ) .

Use the formula of ∫ x n dx = x n+1 n+1 +A , where A is constant.

∫ d dx f( x ) = ∫ ( 4 x 3 − 3 x 4 ) dx f( x )=4 ∫ x 3 dx−3 ∫ x −4 dx =4 x 4 4 −3 x −3 −3 +D = x 4 + 1 x 3 +D (1)

It is given that f( 2 )=0,

Substitute the value of x= 2 in equation (1).

f( 2 )= ( 2 ) 4 + 1 ( 2 ) 3 +D =16+ 1 8 +D D=− 129 8

Substitute the value of D in equation (1).

f( x )= x 4 + 1 x 3 − 129 8

Hence, option (A) is correct.