Find the approximate value of `f(3. 02),` where `f(x)=3x^2+5x+3.`

Options

A. `45.46`
B. `37.46`
C. `27.56`
D. `39.40`

Answer

A

Explanation

Here, we will use the definition of derivatives:

`f'(x) = (f(x+Deltax)-f(x))/((x+Deltax)-x)`

`f'(x) = (f(x+Deltax)-f(x))/(Deltax)`

Here, `x = 3 and Deltax = 0.02`

`:. f'(3) = (f(3+0.02) - f(3))/0.02->(1)`

Here, `f'(x) = 6x+5`

`:. f'(3) = 6(3)+5 = 23`

`f(3) = 3(9)+5(3)+3 = 45 `

...