Chapter 9.4, Problem 36E

### 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 35 and 36, find each derivative at the given x-value (a) with the appropriate rule and (b) with the numerical derivative feature of a graphing calculator. y = 1 + 3 x 2 / 3   at  x  = -8

(a)

To determine

To calculate: The derivative of the function y=1+3x23 at x=8.

Explanation

Given Information:

The function, y=1+3x23 and the variable x=âˆ’8.

Formula Used:

According to sum rule of derivatives,

If f(x)=u(x)+v(x) then,

fâ€²(x)=uâ€²(x)+vâ€²(x)

According to power rule,

If f(x)=xn, then fâ€²(x)=nxnâˆ’1.

According to constant function rule,

If f(x)=c, then fâ€²(x)=0.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x).

Calculation:

The given function is y=1+3x23

(b)

To determine

To calculate: The derivative of the function y=1+3x23 at x=8 by use of graphing calculator.

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