Question

For the linear fucntion y = f(x) = -3x 7, find df/dx at x = -1

Answer 1

The derivative of the function f(x) = -3x + 7, which is a linear function, is constant and equal to the slope of the function. Therefore, df/dx at x = -1 is -3.

Step-by-step explanation:

To find the derivative of a linear function, we use the power rule. The power rule states that for a function of the form y = axⁿ, the derivative is given by

dy/dx = naxⁿ⁻¹.

In this case, the function is

y = -3x + 7,

So the derivative is

dy/dx = -3.

Since we want to find the derivative at x = -1, we substitute -1 into the derivative expression:

dy/dx = -3.

Therefore, the derivative of the function at x = -1 is -3.