How do you calculate the forest area?

The solutions state g(x)=1/3x-2. But how do you get the gradient m=1/3x?

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appletman
11 months ago

y = mx + b

-2 = 0m + b, i.e. b = -2

0=6m-2, i.e. 6m=2, i.e. m=2/6=1/3

Most Northern point of the forest: f(x) = 0 set (maximum).

The forest area it the triangular area plus the integral of function f(x), i.e. the given root function from 0 to 6.

Detection of the stam function by deriving F(x) with product rule and optionally chain rule.

The highway has an angle of 90°, the river has the derivation = slope of f(x) at x = 0.

Dfference of slopes form!

Calculate turning point of f(x). How large is the pitch of the fuction f(x) at the turning point? Set the straight line of the tangent.

Set straight line for the forest path. Your gradient is the negative reciprocal of the tangent pitch!

The point of intersection P is finished.

Tannibi
11 months ago

This is the equation of the footpath.

At 6 km in the x-direction y rises by 2 km, the slope
is therefore 2/6 = 1/3.