whay is the critical number of the fuction G(x)=2x+5
A number where first derivation = 0 is called a critical number.
In this case :
d ( 2 x + 5 ) / dx = =
2 = 0
Critical number of the function G(x)= 2 x + 5 not exist
d ( 2 x + 5 ) / dx = 0
2 = 0
Makes no sense.
That is why critical number not exist.
The critical number of a function corresponds to the x-value(s) where the derivative of the function is equal to zero or undefined. To find the critical number of the function G(x) = 2x + 5, we need to find the derivative of G(x) and set it equal to zero.
Let's find the derivative of G(x) by using the power rule. The power rule states that for a function of the form f(x) = ax^n, the derivative is given by f'(x) = nax^(n-1).
In this case, G(x) = 2x + 5, which can be rewritten as G(x) = 2x^1 + 5. Applying the power rule, the derivative of G(x) is G'(x) = 1 * 2x^(1-1) = 2.
Setting G'(x) equal to zero, we have 2 = 0. However, since 2 is a constant, this equation has no solution. Therefore, there are no critical numbers for the function G(x) = 2x + 5.
In general, linear functions (functions of the form f(x) = mx + b) have no critical numbers because the derivative of a linear function is always a constant (in this case, 2). Critical numbers are more commonly found in non-linear functions.