Chapter 9.4, Problem 18E

### 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 15-18, at the indicated points, find(a) the slope of the tangent to the curve.(b) the instantaneous rate of change of the function. R ( x ) = 16 x + x 2 ,    x → =1

(a)

To determine

To calculate: The slope of the tangent to curve R(x)=16x+x2 at x=1.

Explanation

Given Information:

The provided curve is represented by function R(x)=16x+x2, and the point is x=1.

Formula Used:

The slope of line tangent to the curve y=f(x) at any point x is fâ€²(x).

Sum rule for function f(x)=u(x)+v(x), where u and v are differentiable functions of x, then fâ€²(x)=uâ€²(x)+vâ€²(x).

Power of x rule for a real number n is such that, if f(x)=xn then fâ€²(x)=nxnâˆ’1.

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:

Consider the function, R(x)=16x+x2

Differentiate with respect to x

(b)

To determine

To calculate: The instantaneous rate of change of the function R(x)=16x+x2 at x=1.

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