Calculus 1 : How to find slope by graphing functions
Study concepts, example questions & explanations for Calculus 1
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Example Questions
Example Question #21 : Lines
What is the slope of a line tangent to 
It is impossible to be tangent to that line at that point.
A line is tangent to a point on a curve when its slope is equivalent to the slope of the curve at the point of intersection. Therefore to solve this equation, the slope of the curve at 
The slope of a graph at any point can be found by taking the first derivative. To take the derivative of this equation, we must use the power rule,
We also must remember that the derivative of an constant is 0. By taking the first derivative of the graph equation, we obtain the slope equation
Plugging in 
Example Question #31 : Lines
What is the slope of the curve 
To find the a general formula for the slope of the function 
The slope of the function at 
Example Question #32 : Lines
What is the slope of the line tangent to the function at 
None of these
The slope of a tangent line to a function at a point can be found by taking the derivative of the function and plugging in the point at which the slope is to be found. The derivative of the funtion can be found using the product rule.
The derivative of 
Also, the derivative of a sin function is the cos function.
Example Question #33 : Lines
Find the slope of the line tangent to the function at 
None of these
The slope of the tangent at a certain x is the value of the derivative at that point. The derivative of 
The derivative of the given function is
Plugging in x=3 gives
Example Question #34 : Lines
What is the slope of the tangent line to 
The derivative of a function describes the slope. Therefore, you must first find the derivative of the function, which is 
Then, you plug in the specific x value given in the problem, which is -1:
Therefore, your final answer is -7.
Example Question #35 : Lines
At what 
First, you must find the slope equation of the tangent line to the function, which is just the derivative of the function:
Since that is the slope equation, you need to set that equal to 0 and factor:
Example Question #36 : Lines
The coordinates of the following points are given as follows: 
If a 
If the two lines are perpendicular, then their slopes must be opposite reciprocals. Since both lines are tangent to the curve, 
Example Question #37 : Lines
Find the slope of the following function at 
This problem basically amounts to finding the derivative and evaluating it at the given value. We need to use a couple different techniques to find the derivative of this function but they're all fairly simple. We need the chain rule which says:
and the product rule, which is
So, using these we can calculate our derivative. 
this equals,
and when we plug in 
which can be written as 
Example Question #38 : Lines
If 
To find the slope, you must find the derivative of the function. Remember, when taking the derivative, multiply the exponent by the coefficient and then subtract 1 from the exponent, this is known as the power rule.
Therefore, the derivative is:
Then, to find the slope at 1, just plug 1 into the derivative.
Example Question #39 : Lines
Find the slope of the line through:
The slope (m) between two points is found with the following formula:
We can apply this formula with the points we are given:
This is one of the answer choices.
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