The rate of change of a function with respect to x is known as the slope. The slope is constant for the function y = 19x - 11.
What is differentiation?
The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The functions are as follows;
[tex]\rm a. \ \ y=x^2-5x-14\\\\b. \ \ y=19x-10\\\\c. \ \ y=5^x\\\\d. \ \ y=0.03x^2+11x+1[/tex]
The rate of change of the function is called the slope of that function at a point.
a. [tex]\rm y=x^2-5x-14[/tex]
Differentiate the function with respect to x, then we have
[tex]\rm \dfrac{dy}{dx}=2x-5[/tex]
b. [tex]\rm y=19x-10[/tex]
Differentiate the function with respect to x, then we have
[tex]\rm \dfrac{dy}{dx}=19[/tex]
c. [tex]\rm y=5^x[/tex]
Differentiate the function with respect to x, then we have
[tex]\rm \dfrac{dy}{dx}= ln 5 * 5^x[/tex]
d. [tex]\rm y=0.03x^2+11x+1[/tex]
Differentiate the function with respect to x, then we have
[tex]\rm \dfrac{dy}{dx}=0.06x + 11[/tex]
Thus, the slope is constant for the function y = 19x - 11.
More about the differentiation link is given below.
https://brainly.com/question/24062595
