Elixer said:Homework Statement
f(x) = 2x2 + 4e(5x)
is invertible. Give the slope of the normal line to the graph of f-1 at x = 4.
Homework Equations
(Given in question)
The Attempt at a Solution
I don't know how to solve this question. But , I found the following:-
f(4) = 32 + 4e20
LCKurtz said:But f(4) isn't relevant to the question. The question is about the inverse function's slope at x = 4. Remember that f(0) = 4 means (0,4) is on the graph of y = f(x) and it also means that f-1(4) = 0 and (4,0) is on the graph of y = f-1(x).
The slope of that function at that point is what you are looking for. Does that help?
Elixer said:So, (4,0) lies on the graph of f-1(x),
y = f-1(x)
dy / dx = 1/(4y + 20e(5y))
The slope of a normal to a given function's inverse is the negative reciprocal of the slope of the tangent to the function's inverse at the point of intersection.
To find the slope of a normal to a given function's inverse, first find the slope of the tangent to the function's inverse at the point of intersection. Then, take the negative reciprocal of that slope to find the slope of the normal.
The slope of a normal to a given function's inverse represents the rate of change of the inverse function at a specific point. It also indicates the steepness of the curve of the inverse function at that point.
Yes, the slope of a normal to a given function's inverse can be zero if the inverse function is a horizontal line at that point. This means that the slope of the tangent to the inverse function is undefined, and therefore the negative reciprocal is also undefined.
Yes, the slope of a normal to a given function's inverse is affected by the shape of the original function. If the original function has a steep curve at a specific point, the slope of the normal to the inverse function will also be steep at that point.