Science:Math Exam Resources/Courses/MATH110/April 2017/Question 01 (a)/Solution 1

The first interpretation of a derivative is rate of change. If $f(x)$ represents a quantity at any $x$ then the derivative $f'(a)$ represents the instantaneous rate of change of $f(x)$ at $x=a$.

The second is slope of tangent line.The slope of the tangent line to $f(x)$ at $x=a$ is $f'(a)$ . The tangent line then is given by, $y=f(a)+f'(a)(x-a)$.

answer:

$\color {blue}1.\,rate\,of\,change;\,$

$\color {blue}2.\,slope\,of\,tangent\,line$