Question

8.3x2 + 15x + 5, then the approximate value ofIf f(x)(A) 47.663.02) is(B) 57.66(C) 67.66(D) 77.66

Answer 1

The given function is 3 x 2 +15x+5.

Let, x=3, Δx=0.02 and y=f( x ).

Differentiating given function, we get

dy dx = df( x ) dx = d( 3 x 2 +15x+5 ) dx =6x+15

We know that,

Δy= dy dx Δx (1)

Substitute the value of x and Δx in the above equation (1), we get

Δy=( 6x+15 )Δx =( 6×3+15 )0.02 =0.66

We know that,

Δy=f( x+Δx )−f( x )

The above expression can be rewritten as,

f( x+Δx )=Δy+f( x )(2)

Substitute the values of x, Δx and Δyin the above equation (2), we get

f( x+Δx )=3 x 2 +15x+5+Δy f( 3+0.02 )=3× 3 2 +15×3+5+0.66 f( 3.02 )=77.66

Thus, option (D) is correct.