I have no idea how to do this, can someone please help?
Consider the graphs below, which give m(x) in the left graph, in black, and n(x) in the right graph, in blue. Both functions have a sharp corner at x=50.
Let h(x)=n(m(x)). Find a point x where h'(x)=1.44
x=
40< m(x) < 50
I am sorry Michael this platform does not support inserting diagrams into your question. Thus m(x) and n(x) could be anything. Again, sorry.
To find a point x where h'(x) = 1.44, we need to find the derivative of h(x) with respect to x.
Since h(x) = n(m(x)), we can use the chain rule to find the derivative of h(x).
The chain rule states that if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).
In this case, f(x) = n(x) and g(x) = m(x).
Therefore, h'(x) = n'(m(x)) * m'(x).
To find x where h'(x) = 1.44, we need to solve the equation:
1.44 = n'(m(x)) * m'(x).
Note that we are given a range for m(x) as 40 < m(x) < 50.
To proceed further, we need more information about the specific functions m(x) and n(x) and their derivatives.
To find a point x where h'(x) = 1.44, we need to follow a step-by-step process. Let's break it down:
1. Start with the function h(x) = n(m(x)), which represents the composition of two functions, n(x) and m(x).
2. We know that h'(x) represents the derivative of the function h(x) with respect to x. In other words, it measures the rate of change of h(x) at a particular point x.
3. To find x such that h'(x) = 1.44, we can calculate the derivative of h(x) and set it equal to 1.44.
4. First, find the derivative of h(x) using the chain rule. The chain rule states that if y = f(g(x)), then y' = f'(g(x)) * g'(x). In this case, f(x) is n(x) and g(x) is m(x).
- Differentiating n(x) with respect to x, we get n'(x).
- Differentiating m(x) with respect to x, we get m'(x).
5. Now, apply the chain rule to find the derivative of h(x):
h'(x) = n'(m(x)) * m'(x).
6. Plug in the expression for n'(x) and m'(x) as obtained from the given functions in the graph.
7. Simplify the expression for h'(x) and set it equal to 1.44.
8. Solve the equation h'(x) = 1.44 to find the value(s) of x that satisfy the equation.
Considering the constraints you mentioned, namely 40 < m(x) < 50, you can narrow down the possible values of x to that range. You can calculate h'(x) for various values within this range and check which value(s) give you h'(x) = 1.44.