Identify each x-value at which the slope of the tangent line to the function f(x) = 0.2x2 + 5x − 12 belongs to the interval (-1, 1).

slope of the tangent

The slope of the tangent to the interval (-1 ,1)

m = 4.6 ,5, 5.4

Step-by-step explanation:

Step(i):-

Given function is  f(x) = 0.2 x² + 5 x − 12

Slope of the tangent formula

Let y =  f(x) = 0.2 x² + 5 x − 12 ...(i)

Differentiating equation(i) with respective to 'x' , we get

let x=-1

let x=0

m = 5

let x=1

conclusion:-

slope of the tangent

The slope of the tangent to the interval (-1 ,1)

m = 4.6 , 5,  5.4

since the airplane is moving with constant speed then the distance travelled can be calculated by x=u*t

in km/h would be:

x=640*3.5=2.240 km

in m/s would be:

u=640 km/h= 640.000 m/h =640.000/ 3600 m/s =177.8 m/s

t= 3.5 h= 3.5 * 3600 s=12.600 s

then x=u*t= 177.8*12.600= 2.240.280 m