4th Q Definitions

Question 1

a line that touches a curve at a point, matching the curve’s slope there

Answer 1

Tangent

Question 2

If the slope of the tangent line is POSITIVE, the function is?

Answer 2

increasing at the point

Question 3

If the slope of the tangent line is NEGATIVE, the function is?

Answer 3

decreasing at the point

Question 4

It is the instantaneous rate
of change of a function at a given point.

Answer 4

derivative

Question 5

The derivative of a function at a given value is the?

Answer 5

slope of the
line tangent to the function at that value.

Question 6

*A function f(x) is differentiable at x = c, then?

Answer 6

function
f(x) is continuous at x = c

Question 7

*If a function f(x) is not differentiable at x = c, then?

Answer 7

it may or may not be continuous at x = c

Question 8

*If the function f x is continuous at x = c, then?

Answer 8

it need
not be differentiable at x = c

Question 9

*If the function f(x) is discontinuous at x = c, then?

Answer 9

it is not differentiable at x = c

Question 10

T or F: differentiability implies continuity

Answer 10

True

Question 11

T or F: continuity implies differentiability

Answer 11

False

Question 12

T or F: continuity does NOT imply differentiability

Answer 12

True