Question

Let f(x)= 4.3ˣ +6. (a) Find f' (x), the derivative of f(x), and express it in terms of x. (b) State the domain and range of (x) in interval notation.

Answer 1

The derivative of f(x) = 4.3^x + 6 is f'(x) = 4.3^x * ln(4.3). The domain of f(x) is all real numbers, and the range is all real numbers greater than 6.

Step-by-step explanation:

To find the derivative of f(x) = 4.3x + 6, we use the rule for the derivative of an exponential function, which is f'(x) = axln(a), where a is the base of the exponential function. In our case, the base is 4.3, so f'(x) = 4.3xln(4.3).

For part (b), regarding the domain and range of f(x), the domain of any exponential function is all real numbers, which in interval notation is (-∞, +∞). The exponential function is always positive, and because we add 6 to it, the range starts from 6 and goes to positive infinity. Thus, the range in interval notation is (6, +∞).