Studied by 17 peopleHow do you find "rate of change" if given coordinates?
Find the slope between two coordinates.
How do you find "rate of change" if given a function?
Take the derivative.
How do you find instantaneous rate of change at a point?
Find the derivative function and then substitute the value in for x.
If given the position function, how do you find the velocity function?
Find the first derivative.
If given the velocity function, how do you find the acceleration function?
Find the first derivative.
If given the position function, how do you find the acceleration function?
Find the second derivative.
If asked to find the slope of a tangent line, what are you finding?
Derivative.
If asked to find the slope of a tangent line at a point, what should you do?
Find the derivative function and then substitute the x-value into the derivative function.
Explain the power rule.
Multiply the exponent by the coefficient, write the variable with one less exponent.
How do you find a Horizontal Tangent Line?
Take the derivative. Set the numerator = 0 and solve. Substitute the x value back into the original equation to find y.
How do you find a Vertical Tangent Line?
Take the derivative. Set the denominator = 0 and solve. Substitute the x value back into the original equation to find y.
What is the product rule?
f ' g + g ' f
When do you use the product rule?
When asked to find the derivative and the original problems is a multiplication problem with the two parts consisting of variables.
What is the quotient rule?
(g f ' - f g') / g² or (lowdhi - hidlow)/g²
When do you use the quotient rule?
When asked to find the derivative and the original problems is a division problem with the two parts consisting of variables.
Do you need to use the quotient rule in division problems with a constant in the numerator?
No, move the denominator up.
What's the derivative of y = sin(x) ?
y' = cos (x).
What's the derivative of y = cos (x) ?
y' = -sin(x).
What's the derivative of y = tan(x) ?
y' =sec²(x)
What's the derivative of y = csc(x) ?
y' = -csc(x)cot(x)
What's the derivative of y = sec(x) ?
y' = sec(x)tan(x)
What's the derivative of y = cot(x) ?
y' = -csc²(x)
What is the derivative of a sharp turn? Explain.
DNE because the slope of the left side and right side do not approach the same number .
How do you find the equation of a tangent line?
Find the entire coordinate first by plugging in the x to find y.
Find the derivative function,
plug in the x-value into the derivative to find the slope.
Use the slope and coordinate to write an equation (either point-slope or slope-intercept)
How is speed calculated?
absolute value of the velocity function.
When is speed increasing?
When a(t) and v(t) are the same sign.
When is speed decreasing?
When a(t) and v(t) are opposite signs.
What does "normal line" mean?
Perpendicular
What does d²y/dx² mean?
second derivative
If given a velocity graph, how do you make a velocity sign chart?
Look above and below the axis to find the sign of the actual values.
If given a velocity graph, how do you make an acceleration sign chart?
Look at the slopes of the graph.
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