AP Calculus AB : Derivatives
Study concepts, example questions & explanations for AP Calculus AB
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Example Questions
Example Question #151 : Derivatives
Example Question #31 : Slope Of A Curve At A Point
Find the slope of the tangent line to the following function at x=3:
The slope of the tangent line to a curve is given by the first derivative evaluated at the point of interest.
The first derivative of the function is equal to
and was found using the following rules:
To find the slope of the tangent line at x=3, we simply evaluate the first derivative function at x=3:
Example Question #152 : Derivatives
Find the slope of the curve 
To find the slope of the curve at any point, we take its derivative
We then evaluate ate the point 
Example Question #153 : Derivatives
Find k'(1) if 
First, find the derivative. You should get 
Next, plug in x=1.
You should get 
Example Question #154 : Derivatives
Find the slope of the curve at the specified point:
To find the slope of the curve, we take the derivative of the function:
Evaluating the slope at the specified point, we get
Example Question #54 : Derivative At A Point
Find the normal line to the function 
The normal line to a function at a point is the line perpendicular to its tangent line. The normal line to a function has a slope which is the negative reciprocal of its derivative.
For our function 
We now may plug in our point of 
Our normal line will have the form:
Example Question #55 : Derivative At A Point
If 
First, we take the derivative of the line, which gives us the slope of the curve at any point
Then, we evaluate the slope at the point 
Example Question #155 : Derivatives
Given the equation of the line
To solve the problem, we simply take the derivative of the function and evaluate it at the specified point. The derivative of a line is the slope of the curve, so we do the following
Example Question #163 : Ap Calculus Ab
Find the equation of the line passing through (-1, 1) and perpendicular to the line tangent to the following function at x=4:
To determine the equation of the line, we must first find its slope, which is perpendicular to that of the tangent line to the function. The tangent line to the function at any point is given by the first derivative of the function:
The derivative was found using the following rule:
Evaluating the derivative at the given point, we find that the slope of the tangent line to the function is
However, the negative reciprocal of this - the slope of the tangent line - is
We now can write the equation of the line using point-slope form:
Example Question #164 : Ap Calculus Ab
Find the equation of the line passing through (4, 10) and parallel to the tangent line to the following function at x=2:
To determine the equation of the line, we must first find its slope, which is parallel to that of the tangent line to the function. The tangent line to the function at any point is given by the first derivative of the function:
which was found using the following rules:
Now, we find the slope of the tangent line at the given point by plugging this point into the first derivative function:
Now, we use point-slope form to find the equation of the line:
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