Let f(x)=2x−x2,x∈R. If m and n are respectively the number of points at which the curves y=f(x) and y=f′(x) intersects the x-axis, then the value of m+n is

Question

Let f(x)=2x−x2,x∈R. If m and n are respectively the number of points at which the curves y=f(x) and y=f′(x) intersects the x-axis, then the value of m+n is
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Solution 1

To solve this problem, we need to find the roots of the functions f(x) and f'(x), which represent the points where the curves intersect the x-axis.

Step 1: Find the roots of f(x) f(x) = 2x - x^2 Setting f(x) to 0, we get: 0 = 2x - x^2 This can be factored to: 0 = x(2 - x) Setting each factor equal Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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