Question

For the function y = (x^2 + 1)(x^3 - 9x), at (-3, 0) find the following. (a) the slope of the tangent line (b) the instantaneous rate of change of the function

          For the function y = (x^2 + 1)(x^3 - 9x), at (-3, 0) find the following.
(a) the slope of the tangent line
(b) the instantaneous rate of change of the function

Added by Maria E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/13/2023

Step 1

To do this, we will use the product rule: (uv)' = u'v + uv' Let u = x^2 + 1 and v = x^3 - 9x. Now, we need to find the derivatives of u and v with respect to x: u' = d(u)/dx = d(x^2 + 1)/dx = 2x v' = d(v)/dx = d(x^3 - 9x)/dx = 3x^2 - 9 Now, we can apply the Show more…

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For the function y = (x^2 + 1)(x^3 - 9x), at (-3, 0) find the following: (a) the slope of the tangent line (b) the instantaneous rate of change of the function