Chapter 3.7, Problem 5TE

### Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640

Chapter
Section

### Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

# In Exercises 1-6, use dy to approximate Δy for the function y = f(x) when x changes from x = a to x = b.5. f ( x ) = x 2 + 4 x − 1 ; a = 4, b = 4.1

To determine

To find: The approximate value of the given function.

Explanation

Given information:

The given function is f(x)=x2+4xâˆ’1 .

Formula used:

The approximate change in function f(x) is, Î”[f(x)]=fâ€²(x)Î”x (1)

Calculation:

The value of Î”x in function f(x) changes from a=4 to b=4.1 .

Î”x=bâˆ’a=4.1âˆ’4=0.1

The function is f(x)=x2+4xâˆ’1 .

Differentiate above function with respect to x and get the value of fâ€²(x) .

ddx[f(x)]=ddx(x2+4xâˆ’1)fâ€²(x)=(xâˆ’1)((2x+0)2x2+4)âˆ’x2+4(1âˆ’0)(xâˆ’1)2 (âˆµd(u/v)dx=â€‰â€‰â€‰vdudxâˆ’udvdxv2)=(2x2âˆ’2x2x2+4)âˆ’x2+4(xâˆ’1)2=<

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