What is the equation of the normal line of #f(x)= -2x^2-10/x # at #x=2 #?
1 Answer
Explanation:
Things we need to do:
• Part 1 - Solve for the point at
• Part 2 - Getting the derivative of
• Part 3 - Getting slope of the tangent line at
• Part 4 - Getting slope of the normal line at
• Part 5 - Getting the equation of the normal line at
Part 1 - Solve for the point at
Simply plug substitute
So the point at
Part 2 - Getting the derivative of
By difference rule,
By power rule,
By power rule,
Part 3 - Getting slope of the tangent line at
Part 4 - Getting slope of the normal line at
Since the normal line is the line perpendicular to the tangent line, we can easily find the slope of the normal line by getting the negative reciprocal of the slope of the tangent line.
Part 5 - Getting the equation of the normal line at
We will use the point-slope form to find the equation of the normal line, where
Plug in the slope of the normal line.
Plug in the point