For the function y = (x^3 − 3)(x^2 − 5x + 1) at (2, −25) find the following.
(a) the slope of the tangent line
(b) the instantaneous rate of change of the function

(a)

(b)

Step-by-step explanation:

We have been a function . We are asked to find the instantaneous rate of change of the function and the slope of the tangent line at point .

(a) First of all, we will find the derivative of our given function using product rule.

Now, we will substitute in our derivative function to find slope of tangent line as:

Therefore, the slope of the tangent line is -65 at point .

(b) We know that instantaneous rate of change of the function at a point is equal to the derivative of the function at that point.

We already figured it out that derivative of our given function at is , therefore, the instantaneous rate of change of the function is also at point .

step-by-step explanation:

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step-by-step explanation: