Mathematics: See question in image.Please show workings .

gdahjrvb8hfy in cf h NC fi t47 ur e7ut6...

See question in image.Please show workings .

ayowazzzgood

17.03.2022

see explanation

Step-by-step explanation:

Given f(x) then the derivative f'(x) from first principles is

f'(x) = lim ( h tends to 0 ) $\frac{f(x+h)-f(x)}{h}$

= lim ( h to 0 ) $\frac{3(x+h)^3+2-(3x^3+2)}{h}$

= lim ( h to 0 ) $\frac{3(x^3+3x^2h+3xh^2+h^3)+2-3x^3-2}{h}$

= lim ( h to 0 ) $\frac{3x^3+9x^2h+9xh^2+3h^3-3x^3}{h}$

= lim ( h to 0 ) $\frac{9x^2h+9xh^2+3h^3}{h}$

= lim ( h to 0 ) $\frac{h(9x^2+9xh+3h^3)}{h}$ ← cancel h on numerator/ denominator

= lim ( h to 0 ) 9x²+9xh+3h² ← let h go to zero

f'(x) = 9x²

0,0(0 оценок)