   Chapter 2.7, Problem 23E

Chapter
Section
Textbook Problem

Sketch the graph of a function f for which f(0) = 0, f'(0) = 3, f'(l) = 0, and f'(2) = – 1.

To determine

To sketch: The graph of the function f(x)

Explanation

Given:

The values. f(0)=0,f(0)=3,f(1)=0 and f(2)=1.

Calculation:

Here given values f(0)=0,

That is, the graph of the function f(x) is crosses x-axis at the points x=0.

Note that, f(a) means that the slope of the tangent to the function f(x) at the point (a,f(a)).

The given values f(1)=0.

That is, the slopes of tangent to the function f(x) at (1,f(1)) is zero.

Note that, the slope zero at a point means horizontal tangent line at that point.

Thus, the graph of the function f(x) has horizontal tangent at (1,f(1)).

Note that, the value f(a) means that the instantaneous rate of change of y=f(x) at x when x=a

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