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
you know, posting the same question three times does not get you any points, nor any faster help.
To find a point x where h'(x) = 1.44, we need to differentiate the function h(x) = n(m(x)) first.
To differentiate h(x), we will use the chain rule, which states that if we have a composition of functions, such as h(x) = f(g(x)), then the derivative of h(x) is given by h'(x) = f'(g(x)) * g'(x).
Let's break down the function h(x) = n(m(x)) into its constituent parts:
f(x) = n(x)
g(x) = m(x)
Now, we need to find the derivatives of f(x) and g(x).
Since we do not know the specific functions n(x) and m(x), we cannot directly calculate their derivatives. However, we are given the graphs of m(x) and n(x), so we can estimate the derivatives numerically.
Given that 40 < m(x) < 50, we can see from the graph of m(x) on the left that m(x) is increasing as x increases. Therefore, m'(x) > 0 for 40 < x < 50. However, without more information about the specific function m(x), we cannot determine the exact value of m'(x).
Similarly, looking at the graph of n(x) on the right, we can observe that n(x) is decreasing as x increases in the range 40 < x < 50. Hence, n'(x) < 0 for 40 < x < 50. Again, without additional information about the function n(x), we cannot calculate n'(x) precisely.
Now, to calculate h'(x) using the chain rule, we multiply f'(g(x)) with g'(x). Since we do not know the explicit forms of f(x) and g(x), we cannot calculate their derivatives precisely. Therefore, we cannot determine h'(x) analytically.
Given this information, it may be more helpful to analyze the graphs of m(x) and n(x) visually to estimate a value of x where h'(x) could be approximately equal to 1.44.
Please note that to provide a more accurate answer, more specific information about the functions m(x) and n(x) would be required.