Question

Can someone please help me with this?

Answer 1

x ≈ .690

Step-by-step explanation:

PQ has a slope of
`(y_1 - y_2)/(x_1 - x_2)` =
`(4 - 0)/(0 - (\pi)/(2) )` =
`(-8)/(\pi)`. Thus, the line parallel to line PQ must also have a slope of
`(-8)/(\pi)`.

We know that to find the instantaneous rate of change (slope of tangent line) at any x-coordinate on f, we must find the derivative of f. f'(x) = -4sin(x), so we must find where f'(x) =
`(-8)/(\pi)`

We solve the equation:

-4sin(x) =
`(-8)/(\pi)` ⇒ divide both sides by -4

sin(x) =
`(2)/(\pi)` ⇒ arcsin of both sides

x = arcsin(
`(2)/(\pi)`)

We can plug this into a calculator and get x = .690107091375 ≈ .690