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

4 answers
Question:

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).

Answers

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

 

Step-by-step explanation:


[tex]Identify each x-value at which the slope of the tangent line to the function f(x) = 0.2x2 + 5x − 12[/tex]

-14, -12, -10.5

Step-by-step explanation:

Just answered the question

The slope of the function is given by its derivative. You want to find the values of x such that the derivative is between -1 and 1.

... f'(x) = 0.4x +5

... -1 < 0.4x +5 < 1 . . . . . your requirement for slope

... -6 < 0.4x < -4 . . . . . . subtract 5

... -15 < x < -10 . . . . . . . multiply by 2.5


Any value of x that is between -15 and -10 will be one where the tangent line has a slope between -1 and 1.


_____

The graph shows tangent lines with slopes of -1 and +1. You can see that the slope of the graph of f(x) is between those values when x is between the tangent points.


[tex]How can you tell if the slope of a tangent line belongs to a certain interval? the question is: id[/tex]

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