Math CentralQuandaries & Queries


Question from Maddie, a student:

Find a general equation for a line that touches, but does not pass through the function Y=X2(X squared) + BX+C.

We have two responses for you

Hi Maddie.

A tangent line is a line, so you can construct it using y = mx + b. You can find m by taking the derivative of the function. Then you can use your knowledge that the line passes through (x, x^2 + Bx + C) to find the value of the y intercept (b).

Then just simplify.

Stephen La Rocque



The derivative gives you the slope of the tangent line at any point (X,Y) on the graph of the function. And then you can use the coordinates of that point to find the equation of the line. You can replace Y by what it equals to get the coordinates in terms of X only. Using the slope of the tangent line at (X,Y) obtained earlier, and remembering how to find the equation of a line given its slope and a point it contains (point-slope form), you can complete the question.


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