All GMAT Math Resources
Example Questions
Example Question #1 : Tangent Lines
Determine the equation of the line tangent to the curve at the point ?
To find the equation of a line tangent to a curve at a certain point, we first need to find the slope of the curve at that point. To find the slope of a function at any point, we need its derivative:
Now we can plug in the x value of the given point to find the slope of the function, and therefore the slope of tangent line, at that point:
Now that we have our slope, we can simply plug this value in with the given point to solve for the y intercept of the tangent line:
We have calculated the slope of the tangent line and its y intercept, so the equation for the line tangent to the curve at the point in standard form is:
Example Question #621 : Geometry
Determine the equation of the line tangent to the following curve at the point .
First we find the slope of the tangent line by taking the derivative of the function and plugging in the -value of the point where we want to know the slope:
Now that we know the slope of the tangent line, we can plug it into the equation for a line along with the coordinates of the given point in order to calculate the -intercept:
We now have and , so we can write the equation of the tangent line:
Example Question #2 : Tangent Lines
Find the equation of a line tangent to the curve at the point .
None of the above equations
To find the equation of a line tangent to the curve at the point , we must first find the slope of the curve at the point by solving the derivative at that point:
Given the slope, we can now plug the given point and the slope at that point into the slope-intercept form of the tangent line and solve for the -intercept :
Given our slope, the chosen point, and the -intercept, we have the equation of our tangent line:
Example Question #3 : Calculating The Equation Of A Tangent Line
Find the equation of a line tangent to the curve at the point .
None of the above
To find the equation of a line tangent to the curve at the point , we must first find the slope of the curve at the point by solving the derivative at that point:
Given the slope, we can now plug the given point and the slope at that point into the slope-intercept form of the tangent line and solve for the -intercept :
Given our slope, the chosen point, and the -intercept, we have the equation of our tangent line:
Example Question #622 : Geometry
Determine the equation of the tangent line to the following curve at the point :
First find the slope of the tangent line by taking the derivative of the function and plugging in the x value of the given point to find the slope of the curve at that location:
So the slope of the tangent line to the curve at the given point is . The next step is to plug this slope into the formula for a line, along with the coordinates of the given point, to solve for the value of the y intercept of the tangent line:
We now know the slope and y intercept of the tangent line, so we can write its equation as follows:
Example Question #2 : Tangent Lines
Find the equation of a line tangent to the curve at the point .
None of the above
To find the equation of a line tangent to the curve at the point , we must first find the slope of the curve at the point by solving the derivative at that point:
Given the slope, we can now plug the given point and the slope at that point into the slope-intercept form of the tangent line and solve for the -intercept :
Given our slope, the chosen point, and the -intercept, we have the equation of our tangent line: