Thread: Tangent Line

if anybody could help with this that would be much appreciated:

Find the point on the graph f(x)=4/3x^3 where the tangent line is perpendicular to the line y=-16x+3

Thanks in advance

-Ryan

Originally Posted by compuryan

if anybody could help with this that would be much appreciated:

Find the point on the graph f(x)=4/3x^3 where the tangent line is perpendicular to the line y=-16x+3

Thanks in advance

-Ryan

Remember two lines are perpendicular to one another if and only if their slopes are negative reciprocals of each other.

Thus, means the perpendicular line has slope .

The slope of any given point on the graph is its derivative which is,
.

We need that to be as explained in the first paragraph thus, . Solving we have that . These are the two x-values on the graph where the tangent is perpendicular to this line.