Question

Consider f(x) = 3x² - 2x - 31. a. Compute: f(a) b. Compute and simplify: c. Compute and simplify: d. Compute and simplify: f(a+h) = f(a+h)-f(a) = f(a+h)-f(a) h

Answer 1

`f'(x)=6x-2`

Explanation:

`\displaystyle f'(x)=\lim_(h\rightarrow0)(f(x+h)-f(x))/(h)\\\\f'(x)=\lim_(h\rightarrow0)(3(x+h)^2-2(x+h)-31-(3x^2-2x-31))/(h)\\\\f'(x)=\lim_(h\rightarrow0)(3(x^2+2xh+h^2)-2x-2h-31-3x^2+2x+31)/(h)\\\\f'(x)=\lim_(h\rightarrow0)(3x^2+6xh+3h^2-2h-3x^2)/(h)\\\\f'(x)=\lim_(h\rightarrow0)(6xh+3h^2-2h)/(h)\\\\f'(x)=\lim_(h\rightarrow0)6x+3h-2\\\\f'(x)=6x+3(0)-2\\\\f'(x)=6x-2`