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).

Answer 1

Answer:

slope of the tangent

$\frac{d y}{d x} = 0.2(2 x) + 5 (1)$

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

                        $m = \frac{d y}{d x}$

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

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

conclusion:-

slope of the tangent

$\frac{d y}{d x} = 0.2(2 x) + 5 (1)$

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

m = 4.6 , 5,  5.4

 

Answer 2

Answer:

Step-by-step explanation: