   Chapter 9.4, Problem 37E ### 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 37-40, complete the following.(a) Calculate the derivative of each function with the appropriate formula.(b) Check your result from part (a) by graphing your calculated derivative and the numerical derivative of the given function with respect to x evaluated at x. f ( x ) = 2 x 3 + 5 x − π 4 + 8

(a)

To determine

To calculate: The derivative of the function f(x)=2x3+5xπ4+8 at x=2.

Explanation

Given Information:

The function, f(x)=2x3+5xπ4+8 and the variable x=2.

Formula Used:

According to sum rule of derivatives,

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

f(x)=u(x)+v(x)

According to power rule,

If f(x)=xn, then f(x)=nxn1.

According to constant function rule,

If f(x)=c, then f(x)=0.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Calculation:

The given function is f(x)=2x3+5xπ4+8

(b)

To determine

The derivative of the function f(x)=2x3+5xπ4+8 at x=2 using TI-83 calculator.

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