Answer:
<em>slope of the tangent</em>
<em></em>
<em></em>
<em>The slope of the tangent to the interval (-1 ,1)</em>
<em>m = 4.6 ,5, 5.4</em>
Step-by-step explanation:
<u><em>Step(i):</em></u>-
Given function is f(x) = 0.2 x² + 5 x − 12
Slope of the tangent formula
![m = \frac{d y}{d x}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7Bd%20y%7D%7Bd%20x%7D)
Let y = f(x) = 0.2 x² + 5 x − 12 ...(i)
Differentiating equation(i) with respective to 'x' , we get
![\frac{d y}{d x} = 0.2(2 x) + 5 (1) -0](https://tex.z-dn.net/?f=%5Cfrac%7Bd%20y%7D%7Bd%20x%7D%20%3D%200.2%282%20x%29%20%2B%205%20%281%29%20-0)
let x=-1
![m = \frac{dy}{dx} = 0.2 (2 X -1) +5 = 4.6](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%200.2%20%282%20X%20-1%29%20%2B5%20%3D%204.6)
let x=0
m = 5
let x=1
![m = \frac{dy}{dx} = 0.2 (2 X 1) +5 = 5.4](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%200.2%20%282%20X%201%29%20%2B5%20%3D%205.4)
<u><em>conclusion</em></u>:-
<em>slope of the tangent</em>
<em></em>
<em></em>
<em>The slope of the tangent to the interval (-1 ,1)</em>
<em>m = 4.6 , 5, 5.4</em>