Let f(x) be a polynomial function, whose derivative is given by f'(x). Let line q be the line passing through the point (c, f(C)), whoseslope is f'(C). Then, line q intersects the graph of f(x) only at the point (c, f(c)). (True or False)ATrue, because the slope of line q is the derivative of f(x) at x = c.BFalse, because line q is only locally tangent to the graph of f(x).True, because the line q is the tangent line to the graph of f(x) at the point (c, f(c)).False, because the derivative of f(x) may not be defined at x = c.

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Let f(x) be a polynomial function, whose derivative is given by f'(x). Let line q be the line passing through the point (c, f(c)), whose slope is f'(c). Then, line q intersects the graph of f(x) only at the point (c, f(c)). (True or False)

Let f(x) be a polynomial function, whose derivative is given by f'(x). Let line q be the line passing through the point (c, f(c)), whose slope is f'(c). Then, line q intersects the graph of f(x) only at the point (c, f(c)). (True or False)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.CR: Chapter 4 Review

Problem 4CR: Determine whether each of the following statements is true or false, and explain why. The derivative...

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Question

Let f(x) be a polynomial function, whose derivative is given by f'(x). Let line q be the line passing through the point (c, f(C)), whose
slope is f'(C). Then, line q intersects the graph of f(x) only at the point (c, f(c)). (True or False)
A
True, because the slope of line q is the derivative of f(x) at x = c.
B
False, because line q is only locally tangent to the graph of f(x).
True, because the line q is the tangent line to the graph of f(x) at the point (c, f(c)).
False, because the derivative of f(x) may not be defined at x = c.

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