1, We are given f ( x ) 9 x 2 and f ' ( x ) 18 x (a) Find the instantaneous rate of change of f ( x )at x 2 (b) Find the slope of the tangent to the graph of y f ( x )at x 2 (c) Find the point on the graph of y f ( x )at x 2 2,We are given f ( x ) 8 x 2 and f ' ( x ) 16 x Exercise (a) Find the instantaneous rate of change of f ( x )at x 3 Exercise (b) Find the slope of the tangent to the graph of y f ( x )at x 3 Exercise (c) Find the point on the graph of y f ( x )at x 3 3,In Example 6 in this section, we were given f ( x ) 3 x 2 2 x 11 and found f ' ( x ) 6 x 2 (a)Find the instantaneous rate of change of f ( x )at x 9 (b)Find the slope of the tangent to the graph of y f ( x )at x 9 (c)Find the point on the graph of y f ( x )at x 9 4Let f ( x ) 4 x 2 2 x (a) Use the definition of derivative and the Procedure Example box in this section to find the derivative f ' ( x ) (b) Find the instantaneous rate of change of f ( x ) at x 1 (c) Find the slope of the tangent to the graph of y f ( x )at x 1 (d) Find the point on the graph of y f ( x )at x 1 5 Consider the following f ( x ) 3 x 2 6 x 19 (a) Find the derivative, by using the definition f ' ( x ) (b) Find the instantaneous rate of change of the function at any value f ' ( x ) Find the instantaneous rate of change of the function at the value x 4 f ' (4) (c) Find the slope of the tangent at the value x 4 6, p ( q ) 2 q 2 q 7 (a) Find the derivative, by using the definition p' ( q ) (b) Find the instantaneous rate of change of the function at any value p ' ( q ) Find the instantaneous rate of change of the function at the value q 11 p ' (11) (c) Find the slope of the tangent at the value q 11 7 Use the given table to approximate f' ( a ) as accurately as you can f' (13) x 12 012 991313 1 a 13 f ( x )1 4717 4217 1722 86 8 A point ( a , b ) on the graph of y f ( x )is given, as is the equation of the line tangent to the graph of f ( x )at ( a , b ) is given Find f ' ( a )and f ( a ) (Give exact answers Do not round )(4,13) 4 x 5 y 81 f (4) f ' (4) 9, A point ( a , b ) on the graph of y f ( x )is given, as is the equation of the line tangent to the graph of f ( x )at ( a , b ) is given Find f ' ( a )and f ( a ) (5,6) 7 x 2 y 47 10 If the instantaneous rate of change of f ( x ) at (4,5) is9, write the equation of the line tangent to the graph of f ( x ) at x 4 (Let x be the independent variable and y be the dependent variable ) 11,If the instantaneous rate of change of g ( x ) at(1,2)is 1 2, write the equation of the line tangent to the graph of g ( x ) at x 1 (Let x be the independent variable and y be the dependent variable ) 12 Consider the function f ( x ) x 2 x and the point(2,6) (a) Find the slope of the tangent to the graph of f ( x ) at any point (b) Find the slope of the tangent at the given point (c) Write the equation of the line tangent to the graph of f ( x ) at the given point (Let x be the independent variable and y be the dependent variable ) 13 Consider the function f ( x ) x 3 5and the point(1,6) (a) Find the slope of the tangent to the graph of f ( x ) at any point (b) Find the slope of the tangent at the given point (c) Write the equation of the line tangent to the graph of f ( x ) at the given point (Let x be the independent variable and y be the dependent variable )

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Question: 1, We are given f ( x ) =9 x 2 and f ' ( x ) =18 x . (a) Find the instantaneous rate

1, We are givenf(x) =9x²andf'(x) =18x.

(a) Find the instantaneous rate of change off(x)atx=2.

(b) Find the slope of the tangent to the graph ofy=f(x)atx=2.

2,We are givenf(x) =8x²andf'(x) =16x.

Exercise (a)Find the instantaneous rate of change off(x)atx=3.

Exercise (b)Find the slope of the tangent to the graph ofy=f(x)atx=3.

Exercise (c)Find the point on the graph ofy=f(x)atx=3.

3,In Example 6 in this section, we were givenf(x) = 3x²+ 2x+ 11 and foundf'(x) = 6x+ 2.

(a)Find the instantaneous rate of change off(x)atx=9.

(b)Find the slope of the tangent to the graph ofy=f(x)atx=9.

(c)Find the point on the graph ofy=f(x)atx=9.

4Letf(x) =4x²2x.

(a) Use the definition of derivative and the Procedure/Example box in this section to find the derivative.f'(x) =

(b) Find the instantaneous rate of change off(x) atx=1.

(d) Find the point on the graph ofy=f(x)atx=1.

5 Consider the following. f(x) =3x²+6x19

(a) Find the derivative, by using the definition.f'(x) =

(b) Find the instantaneous rate of change of the function at any value.f'(x) =

Find the instantaneous rate of change of the function at the valuex=4.f'(4) =

6,p(q) =2q²+q+7

(a) Find the derivative, by using the definition.

p'(q) =

(b) Find the instantaneous rate of change of the function at any value.

p'(q) =

Find the instantaneous rate of change of the function at the valueq=11.

p'(11) =

7 Use the given table to approximatef'(a) as accurately as you can.

f'(13) =x12.012.991313.1a= 13f(x)1.4717.4217.1722.86

8 A point (a,b) on the graph ofy=f(x)is given, as is the equation of the line tangent to the graph off(x)at (a,b) is given. Findf'(a)andf(a).(Give exact answers. Do not round.)(4,13); 4x5y=81

f(4)=

f'(4)=

9, A point (a,b) on the graph ofy=f(x)is given, as is the equation of the line tangent to the graph off(x)at (a,b) is given. Findf'(a)andf(a).

(5,6);7x2y=47

10 If the instantaneous rate of change off(x) at (4,5) is9, write the equation of the line tangent to the graph off(x) atx=4. (Letxbe the independent variable andybe the dependent variable.)

11,If the instantaneous rate of change ofg(x) at(1,2)is 1/2, write the equation of the line tangent to the graph ofg(x) atx=1.(Letxbe the independent variable andybe the dependent variable.)

12 Consider the functionf(x) =x²+xand the point(2,6).

(a) Find the slope of the tangent to the graph off(x) at any point.

(b) Find the slope of the tangent at the given point.

(c) Write the equation of the line tangent to the graph off(x) at the given point. (Letxbe the independent variable andybe the dependent variable.)

13 Consider the functionf(x) =x³+5and the point(1,6).

(a) Find the slope of the tangent to the graph off(x) at any point.

(b) Find the slope of the tangent at the given point.

(c) Write the equation of the line tangent to the graph off(x) at the given point. (Letxbe the independent variable andybe the dependent variable.)

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