Free Printable AROC, Secant lines, Tangent Lines in Calculus

1.

When you find the average rate of change over an interval, you are finding the slope of the (a) line on that interval.

2.

When you are finding the instantaneous rate of change at a single point, you are finding the slope of the (a) line at that point.

3.

Find the average rate of change of Pete's height from 3 years old to 5 years old.

a)

2 inches per year

b)

8 inches per year

c)

2 years

d)

4 inches per year

4.

The average rate of change on an interval is the...

a)

slope of the secant line on that interval

b)

slope of the tangent line on that interval

c)

slope of the cosecant line on that interval

d)

slope of the normal line on that interval

5.

If the slope of the tangent line is 0, what does that mean with about the graph of the tangent line?

a)

Tangent line is vertical

b)

Tangent line has a positive slope

c)

Tangent line is horizontal

d)

Tangent line has a negative slope

6.

Which of the following graphs has the largest average rate of change from -1 to 2?

a)

b)

c)

d)

7.

Find the average rate of change over

\left[-1,4\right]

a)

-5/7

b)

7/5

c)

-7/5

d)

5/7

8.

State the slope of the line given.

a)

Positive

b)

Negative

c)

Zero Slope

d)

Undefined

9.

Find the difference quotient for $f\left(x\right)=x^2-2x-3$ .

a)

2a - 2

b)

2a - h - 2

c)

2a + h - 2

d)

2h - 2

10.

If $f\left(x\right)=x+5$ then find $\frac{f\left(x+\Delta x\right)-f\left(x\right)}{\Delta x}$

a)

1

b)

$x+\Delta x+5$

c)

$-x\ -\ 5$

d)

$\frac{\Delta x-5}{\Delta x}$

11.

If $g\left(x\right)=x^2$ then what is $\frac{g\left(x+\Delta x\right)-g\left(x\right)}{\Delta x}$ ?

a)

$x^2+2x\Delta x+\Delta x^2$

b)

$2x^2+2x\Delta x+\Delta x^2$

c)

$2x+\Delta x$

d)

$2+\Delta x$

12.

Given the following _____________line, find the instantaneous rate of change at $x=1$ .

a)

secant, $2$

b)

tangent, $2$

c)

secant ,

\frac{1}{2}

d)

tangent, $\frac{1}{2}$

13.

The derivative is...

a)

slope of the secant line

b)

slope of the tangent line

c)

slope of the cosecant line

d)

slope of the normal line

14.

Given the following graph with tangent lines, at which

x-value is the derivative equal to zero?

a)

$x=-8$

b)

$x=-5$

c)

$x=-1.7$

d)

$x=1$

15.

Find the average rate of change on the interval $\left[a,a+h\right]$

a)

$\left(\frac{f\left(a+h\right)-f\left(a\right)}{a}\right)$

b)

$\left(\frac{f\left(a+h\right)-f\left(a\right)}{h}\right)$

c)

$\left(\frac{f\left(a\right)-f\left(a+h\right)}{h}\right)$

d)

$\frac{f\left(a+h\right)}{f\left(a\right)}$

16.

Find the instantaneous rate of the change at $x=a$ .

a)

$\lim_{a\rightarrow0}\left(\frac{f\left(a+h\right)-f\left(a\right)}{a}\right)$

b)

$\lim_{h\rightarrow0}\left(\frac{f\left(a+h\right)-f\left(a\right)}{h}\right)$

c)

$\lim_{h\rightarrow0}\left(\frac{f\left(a\right)-f\left(a+h\right)}{h}\right)$

d)

$\lim_{a\rightarrow0}\left(\frac{f\left(a+h\right)}{f\left(a\right)}\right)$

17.

FInd the equation of the secant line on the interval

\left[-2,1\right]

a)

$y=1$

b)

$y-3=1\left(x+1\right)$

c)

$y-3=1\left(x-1\right)$

d)

$y-2=1\left(x-0\right)$

18.

Write the equation of the tangent line drawn at
$x=1$

a)

$y=1$

b)

$x=1$

c)

undefined

d)

$y=2x+1$

AROC, Secant lines, Tangent Lines in Calculus

Total questions: 18

Worksheet time: 3hrs 56mins

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