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trasher [3.6K]
3 years ago
8

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).

Mathematics
2 answers:
Misha Larkins [42]3 years ago
7 0

Answer:

<em>slope of the tangent</em>

<em></em>\frac{d y}{d x} = 0.2(2 x) + 5 (1)<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}

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

let x=-1

m = \frac{dy}{dx} = 0.2 (2 X -1) +5 = 4.6

let x=0

m = 5

let x=1

m = \frac{dy}{dx} = 0.2 (2 X 1) +5 = 5.4

<u><em>conclusion</em></u>:-

<em>slope of the tangent</em>

<em></em>\frac{d y}{d x} = 0.2(2 x) + 5 (1)<em></em>

<em>The slope of the tangent to the interval (-1 ,1)</em>

<em>m = 4.6 , 5,  5.4</em>

 

adoni [48]3 years ago
3 0

Answer:

Step-by-step explanation:

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