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
At x=40, m(x)=0.8 and n(0.8)=1.44. Therefore, x=40 is the point where h'(x)=1.44.
To find the point x where h'(x) = 1.44, we need to find the derivative of the function h(x) = n(m(x)) and set it equal to 1.44.
The function h(x) is the composition of two functions, n(x) and m(x). So, we can apply the chain rule to find its derivative.
The chain rule states that if we have a composite function h(x) = f(g(x)), the derivative of h(x) with respect to x is given by h'(x) = f'(g(x)) * g'(x).
In this case, h(x) = n(m(x)), so let's start by finding the derivative of n(x) with respect to x.
Since the graph of n(x) is given, we can see that it is a constant function in the interval 40 < m(x) < 50. So, its derivative is zero in that interval.
Now, let's find the derivative of m(x) with respect to x. Since the graph of m(x) is given, we can see that it is a linear function with a sharp corner at x = 50. So, its derivative is not defined at x = 50.
Therefore, h'(x) = n'(m(x)) * m'(x) is zero for x in the interval 40 < m(x) < 50.
Based on this information, we can conclude that there is no point x in the interval 40 < m(x) < 50 where h'(x) = 1.44.
To find the point x where h'(x) = 1.44, we need to follow a systematic process. Let's break it down step by step:
Step 1: Determine the value of m(x) when h'(x) = 1.44 in the range 40 < m(x) < 50.
To do this, we need to find the x-value(s) where m(x) equals a value in the range 40 < m(x) < 50. You can visually inspect the left graph provided to identify where m(x) is between 40 and 50. Look for the section of the black curve that lies between x = 40 and x = 50.
Step 2: Plug the x-value(s) found in Step 1 into h(x) = n(m(x)).
Take the x-value(s) you identified from Step 1 and substitute them into the equation h(x) = n(m(x)). This will yield the corresponding value(s) of h(x) for those x-values.
Step 3: Calculate the derivative of h(x) with respect to x.
Now that we have the function h(x), find its derivative with respect to x. This will give us h'(x), which represents the rate of change of h(x) with respect to x.
Step 4: Set up the equation h'(x) = 1.44 and solve for x.
Since we want to find the x-value(s) where h'(x) = 1.44, we can set up the equation h'(x) = 1.44 and solve for x. Rearrange the equation h'(x) = 1.44 and solve to find the x-value(s) that satisfy the equation.
By following these steps, you will be able to find the point x where h'(x) = 1.44 in the given scenario.