Unit V Big Questions

The formula for the difference quotient comes from the derivative, that represents a formula which tells us the slope of the line that is tangent to any graph at any point. So, to get to the derivative, we must first evaluate the difference quotient. To do this, we find f(x+h), simplify f(x+h)-f(x), and divide the result from the previous step by h. Also, the slope of tangent line to a graph is the same as saying the derivative of a graph because the slope and tangent of a graph are on a and the same. To find the derivative, we evaluate the difference quotient as h approaches 0. Now, when we say the derivative, we say f prime of x (f'(x)) because this is a new equation. To find the slope of the tangent line to f(x) at a specific point, we find the derivative and plug in the x value of the point whose slope of the tangent line we are looking for. To find the equation of the tangent line at a specific point, we go even further and take the slope of the point given at the tangent line and use y=mx+b and find the whole equation with what we have. To find when the tangent line is horizontal, we find the first derivative of f(x), set it equal to zero to represent when the slope of f(x) is horizontal (0) and solve the resulting equation and get values of x where the tangent line would be horizontal.