   Chapter 9, Problem 40RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 40 and 41, decide whether the statements are true or false. lim h → 0 f ( x + h ) − f ( x ) h gives the formula for the slope of the tangent and the instantaneous rate of change of f(x) at any value of x.

To determine

Whether the provided statement, “limh0f(x+h)f(x)h gives the formula for the slope of the tangent and the instantaneous rate of change of f(x) at any value of x” is true or false.

Explanation

Consider the provided statement, “limh0f(x+h)f(x)h gives the formula for the slope of the tangent and the instantaneous rate of change of f(x) at any value of x”.

The slope of the tangent is equal to the derivative of the equation of the surface, to which the line is tangent to.

The instantaneous rate of change represents the change in the function after an instance, which is also found using the formula for derivative.

The formula for derivative is,

limh0f(x+h)f

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