Question

Consider the following. g(x) = 3x² - 4; h(x) = 1.6^x

(a) Write the product function. f(x) =
(b) Write the rate-of-change function. f'(x) =

Answer 1

The product function is obtained by multiplying the two given functions together, f(x) = (3x² - 4) * 1.6^x. The rate-of-change function represents the derivative of the function f(x). To find f'(x), we use the product rule and the power rule of differentiation.

Step-by-step explanation:

The product function, f(x), is obtained by multiplying the two given functions, g(x) and h(x), together. In this case, f(x) = g(x) * h(x). So, f(x) = (3x² - 4) * 1.6^x.

The rate-of-change function, f'(x), represents the derivative of the function f(x). To find f'(x), we need to take the derivative of f(x) with respect to x. In this case, f'(x) = (d/dx)((3x² - 4) * 1.6^x).

To evaluate this derivative, we can use the product rule and the power rule of differentiation. Applying these rules, we can find f'(x) = (6x - 0) * 1.6^x + (3x² - 4) * ln(1.6) * 1.6^x.