Answer:
slope of the tangent
[tex]\frac{d y}{d x} = 0.2(2 x) + 5 (1)[/tex]
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
[tex]m = \frac{d y}{d x}[/tex]
Let y = f(x) = 0.2 x² + 5 x − 12 ...(i)
Differentiating equation(i) with respective to 'x' , we get
[tex]\frac{d y}{d x} = 0.2(2 x) + 5 (1) -0[/tex]
let x=-1
[tex]m = \frac{dy}{dx} = 0.2 (2 X -1) +5 = 4.6[/tex]
let x=0
m = 5
let x=1
[tex]m = \frac{dy}{dx} = 0.2 (2 X 1) +5 = 5.4[/tex]
conclusion:-
slope of the tangent
[tex]\frac{d y}{d x} = 0.2(2 x) + 5 (1)[/tex]
The slope of the tangent to the interval (-1 ,1)
m = 4.6 , 5, 5.4
