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 .

what? ?

what type of question is thiss

step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq