All AP Calculus BC Resources
Example Questions
Example Question #1 : Derivative At A Point
Evaluate the first derivative if
and .
First we must find the first derivative of the function.
Because the derivative of the exponential function is the exponential function itelf, or
and taking the derivative is a linear operation,
we have that
Now setting
Thus
Example Question #3 : Derivative At A Point
Find the rate of change of f(x) when x=3.
Find the rate of change of f(x) when x=3.
To find a rate of change, we need to find the derivative.
First, recall the following rules:
We can apply these two derivative rules to our function to get our first derivative. Then we need to plug in 3 for x and solve.
So, our answer is 105.26
Example Question #63 : Derivatives
Evaluate .
To find , substitute and use the chain rule:
So
and
Example Question #43 : Derivatives
What is the equation of the line tangent to the graph of the function
at the point ?
The slope of the line tangent to the graph of at is
, which can be evaluated as follows:
The equation of the line with slope through is:
Example Question #2 : Derivative At A Point
What is the equation of the line tangent to the graph of the function
at the point ?
The slope of the line tangent to the graph of at is
, which can be evaluated as follows:
, the slope of the line.
The equation of the line with slope through is:
Example Question #63 : Derivative Review
What is the equation of the line tangent to the graph of the function
at ?
The slope of the line tangent to the graph of at is
, which can be evaluated as follows:
, the slope of the line.
The equation of the line with slope through is:
Example Question #1194 : Calculus Ii
What is the equation of the line tangent to the graph of the function
at the point ?
The slope of the line tangent to the graph of at the point is , which can be evaluated as follows:
The line with this slope through has equation:
Example Question #4 : Derivative At A Point
What is the equation of the line tangent to the graph of the function
at the point ?
The slope of the line tangent to the graph of at the point is , which can be evaluated as follows:
The line with slope 28 through has equation:
Example Question #83 : Derivative Review
Given the function , find the slope of the point .
The slope cannot be determined.
To find the slope at a point of a function, take the derivative of the function.
The derivative of is .
Therefore the derivative becomes,
since .
Now we substitute the given point to find the slope at that point.
Example Question #1 : Derivative At A Point
Find the value of the following derivative at the point :
To solve this problem, first we need to take the derivative of the function. It will be easier to rewrite the equation as from here we can take the derivative and simplify to get
From here we need to evaluate at the given point . In this case, only the x value is important, so we evaluate our derivative at x=2 to get.
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