Chapter 9.5, Problem 21E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# In Problems 21 and 22, at the indicated point for each function, find(a) the slope of the tangent line.(b) the instantaneous rate of change of the function. y = x 2 + 1 x + 3 at (2, 1 )

(a)

To determine

To calculate: The slope of the tangent line to the graph of the function y=(x2+1)x+3 at point (2,1).

Explanation

Given Information:

The provided function is y=(x2+1)x+3.

Formula Used:

As per the quotient rule, if two functions are given in the form f(x)g(x), then the derivative is given as:

ddx(fg)=fâ€²â‹…gâˆ’gâ€²â‹…fg2

The slope of the function is the first derivative of the function.

Calculation:

Consider the provided function y=(x2+1)x+3.

For the derivative of y=(x2+1)x+3, follow the steps:

Consider f(x)=(x2+1) and g(x)=x+3.

Apply the quotient rule of the expression,

ddx(fg)=ddx(x2+1x+3)=(x+3)â‹…ddx(x2+1)âˆ’(x2+1)â‹…ddx(x+3)(x+3)2

Evaluate the expression further,

ddx(fg)=(x+3)â‹…ddx(x2+1)âˆ’(x2+1)â‹…dd

(b)

To determine

To calculate: The instantaneous rate of change of the function y=(x2+1)x+3 at point (2,1).

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