Question

Let f(x) = sin (x) 1) Find the average rate of change in f over [ 0, pi/6 ] 2) Find the equation for the corresponding secant line How should i solve this??

Answer 1

(1) Average rate of change is `0.955`
(2) Equation of tangent is `3x-piy=0`

Explanation:

Average rate of change is the ratio of change in the value of the function divided by the change in the value of parameter of the function over a given interval.

For example, we have a function `f(x)` and want its average rate of change over interval `[a,b]`, then average rate of change is `(f(b)-f(a))/(b-a)`.

In the given function `f(x)=sinx` over `[0,pi/6]`, we have `f(0)=0` and `f(pi/6)=0.5` and hence

(1) average rate of change is `(0.5-0)/(pi/6-0)=0.5/(pi/6)=3/pi=0.955`

(2) equation of tangent is the equation of line joining `(0,0)` and `(pi/6,0.5)` i.e.

`(y-0)/(0.5-0)=(x-0)/(pi/6-0)`

or `y/0.5=(6x)/pi` or `3x-piy=0`