1.2 the slope of a tangent to a curve Flashcards
how to calculate the slope of a line given 2 coordinates
label the points x1, y1, x2, y2
use the formula m=y2=y1/x2-x1
how to determine the slope of a perpendicular line given an equation in y intercept form?
jot down the slope m=3
slope of perpendicular line will be the reciprocal and opposite sign of the original slope m=-1/3
how to determine the slope of a perpendicular line given an equation in standard form?
convert standard into slope y intercept form by isolating y variable, diving coefficient of y variable on both sides, simplify by reducing
use that same steps as you would for slope y intercept form to find the slope of the perpendicular line of the equation
what is the difference quotient formula?
f(x+h)-f(x)/h
write the limit approaches 0 for each step
when is the difference quotient used?
used to calculate the slope between two points otherwise known as the slope of the secant line
how to find the slope when x is a specific number
use x in the
how to find the slope when x is a specific number
use x value in the f(x+h)-f(x)/h formula
what is the sum of cubes
a^3+b^3=(a+b)(a^2-ab+b^2)
what is the difference of cubes?
a^3-b^3=(a-b)(a^2+ab+b^2)
what happens when you multiply a rational to the same rational?
the numbers stay the same but the rational is removed
how do you find the slope of the secant?
m=y2-y1/x2-x1
how to determine the slope of the tangent to the curve at a given x value?
use difference quotient formula f(x+h)-f(x)/h and use the given x value from the coordinate to substitute x in the formula
plug the brackets into the original equation as you normally would
what is slope?
the measure of steepness
what is tangent?
a straight line that touches a curve at a specific point
how do you determine the equation of the tangent given a coordinate?
find the derivative
plug x value in coordinate into derivative to find slope at that point
use y=mx+b, the coordinate and the new found slope to isolate b and find the value of b
make the equation
