1. We are given f(x) =9x²andf'(x) =18x.

(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.

(x,y) =

2. In Example 6 in this section, we were given

f(x) = 3x²+ 2x+ 11

and found

f'(x) = 6x+ 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.

(x,y) =

3. Let f(x) =5x²3x.

(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) 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

(x,y) =

4.T he tangent line to the graph off(x) at x=2 is shown. On the tangent line,Pis the point of tangency andAis another point on the line.(a) Find the coordinates of the pointsPandA.

(b) Use the coordinates ofPandAto find the slope of the tangent line. (Give an exact answer. Do not round.) (c) Find f'(2). (Give an exact answer. Do not round.) (d) Find the instantaneous rate of change off(x) atP. (Give an exact answer. Do not round.)

5. The tangent line to the graph of f(x) at x = 1 is shown. On the tangent line, P is the point of tangency and A is another point on the line.

(a) Find the coordinates of the points P and A.

6. Consider the following. f(x) = 5x² + 5x 13

(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 = 3.

f'(3) =

(c) Find the slope of the tangent at the value x = 3.

7. Consider the following. p(q) = 2q² + q + 6

(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 = 9.

p'(9) =

(c) Find the slope of the tangent at the value q = 9.

8. If the instantaneous rate of change of f(x) at (6, 5) is 9, write the equation of the line tangent to the graph of f(x) at x = 6. (Let x be the independent variable and y be the dependent variable.)

9. 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.)