Question

Sketch the graph of a function that is continuous on (1, 5) and has the given properties.

9. Absolute minimum at 5, absolute maximum at 2, local maximum at 3, local minimum at 2 and 4.

Short answer

The graph is sketched.

Step-by-step solution

Given data

The given function is the value of absolute minimum is at 5, absolute maximum is at 2, local maximum at 3, local minimum at 2 and 4.

Concept of Differentiation

Differentiation is a method of finding the derivative of a function. Differentiation is a process, where we find the instantaneous rate of change in function based on one of its variables.

Sketch the graph

Let \(x\) be represented in the \(x\)-axis and the value of \(f(x)\) be represented in the \(y\)-axis.

Since the absolute maximum occurs at the point 5, choose the greatest point on the \(x\)-axis. That is, mark the point on \((5,3)\). Since the absolute minimum occurs at the point 2, choose the least integer value on \(y\)-axis. That is, mark the point on \((2,1)\).

Since the local maximum occurs at the point 3, plot the point on \((3,2)\).

Since the local minima occur at 3 and 4, plot the point on \((2,1)\) and \((4,1)\). The graph of the given function is:

From Figure, it is observed that the absolute maximum occurs at \(x = 5\), absolute minimum occurs at \(x = 2\), local maximum occurs at \(x = 3\) and local minima occurs at \(x = 2\) and \(x = 4\).