Generate Quiz 697D74F672D14

Consequently, a point where the function neither increases nor decreases and the second derivative is zero is best described as a stationary point.

The right response is a) 2ln(3) × 3^(2x).

The power rule of differentiation and the chain rule can be used to determine the derivative of the function f(x) = 3^(2x).

According to the power rule, a function with the formula f(x) = a^g(x) has the following derivative:

d/dx (a^g(x)) = a^g(x) × ln(a) × g'(x)

In this case, we have f(x) = 3^(2x), where a = 3 and g(x) = 2x.

Using the power rule:

f'(x) = d/dx (3^(2x))

= 3^(2x) × ln(3) × 2

= 2ln(3) × 3^(2x)

Consequently, 2ln(3) × 3^(2x) is the derivative of 3^(2x).

An implicit relationship between the variables x and y is represented by the function f(x, y) = c, where c is a constant. Implicit differentiation is the proper technique to employ in order to differentiate such a function.

Implicit differentiation is the process of treating the other variable as a dependent variable while differentiating both sides of the equation with regard to a selected independent variable. This enables us to determine the function’s derivative without having to explicitly solve for one of the variables.

The following are the steps to carry out implicit differentiation on the function f(x, y) = c:

With regard to the selected independent variable, usually x, differentiate both sides of the equation.

To deal with the differentiation of the dependent variable y with respect to x, use the chain rule.

To find the derivative df/dx, rearrange the resulting equation.

The function f(x, y) = c can be differentiated correctly using this implicit differentiation method since it enables us to determine the derivative without explicitly solving for y in terms of x.

The other methods, like Newton’s method, the product rule, and the chain rule, are not suitable for differentiating the given function form.

Using the product rule, this can be resolved with ease, and option B is the result.