Use the limit definition to compute the derivative of the function f(x)=32/31−x at x=−16, and find an equation of the tangent line

The derivative of the function at   equals .

The equation of the tangent line that passes through the point is .

Step-by-step explanation:

From Differential Calculus we remember the following definition of derivative, :

(Eq. 1)

Where is the function evaluated at , dimensionless.

If we know that , then is:

(Eq. 2)

Now we proceed to expand (Eq. 1):

(Eq. 1b)

(Eq. 3)

And the derivative is evaluated at :

The derivative of the function at   equals .

This value represents the slope of the tangent line that passes through , and value of is now found:

The tangent line is represented by the following model:

(Eq. 4)

Where:

- Slope, dimensionless.

- y-Intercept, dimensionless.

- Independent variable, dimensionless.

- Dependent variable, dimensionless.

If we know that , and , the y-Intercept is:

(Eq. 4b)

The equation of the tangent line that passes through the point is .

its a little blurry tbh

step-by-step explanation:

d is the correct answer

step-by-step explanation:

x= 8 because 3x = 3 * 8, and 3*8 = 24