Question

Use the definition of the derivative to find the derivative of: f(t)=14−5tf(t)=14−5t.

f′(t)=
f′(t)=

Answer 1

`\bf f(t)=14-5t\qquad \qquad \stackrel{d e f in i tion~of~a~derivative}{\lim\limits_(h\to 0)~\cfrac{f(t+h)-f(t)}{h}} \\\\\\ \lim\limits_(h\to 0)~\cfrac{[14-5(t+h)]~~-~~[14-5t]}{h}\implies \lim\limits_(h\to 0)~\cfrac{\underline{14-5t}-5h\underline{-14+5t}}{h} \\\\\\ \lim\limits_(h\to 0)~\cfrac{-5\underline{h}}{\underline{h}}\implies -5`