Equation of the Tangent Line
A line that intersects a curve at a minimum of two distinct points.
Secant line!
Bonus $50 if you can define a tangent line.
Find the derivative of f(x) = x+3 using limits!
= 1
What is f'(x) of f(x) = √4
f'(x) = 0
True or false?
Where a function is differentiable it is continuous.
True!
Where a derivative exists the function is continuous
If the equation of the tangent line is
y - f(c) = mtan(x-c)
y - 9 = 2(x-1)
What is the equation of the normal line? (and put in explicit form)
y = (-1/2)x + (19/2)
What is f'(x) of f(x) = x
f'(x) = 1
True or False?
Discontinuity means that the function is differentiable.
False! Discontinuity at a point means that the function is not differentiable at that point.
Can you explain why for a bonus $50?
Find the equation of the tangent line f(x) = 2x+1 at c=2
slope = 2
using y-f(c)=mtan(x-c)
y - 5 = 2(x-2)
y = 2x+1
What is f'(x) of f(x) = 4x4 + 2x6
f'(x) = 16x3+12x5
True of false?
A continuous function is always differentiable.False!
A continuous function can still have non-existent derivatives
An equation of the tangent line of a function at (6,2) is y=(1/6)x +1
What is f '(6)?
f'(6) = 1/6
Remember that mtan=f'(c)
Allana has to put this one on the board bc she refuses to pay for the jeopardy subscription LOLOL
Since the one sided limits are not equal, the function does not have a derivative at c = -1
The limit from the left = -1
The limit from the right = 2
What is the derivative of f(x) = 3x + 5 +2x4 - 3ex
f'(x) = 3 + 8x3- 3ex
Is there a derivative where a function has a sharp corner?
No!
Find the equation of the tangent line of
f(x) = 1/(x+2) at the point (1, 1/3)
The slope is -1/9
So the equation is
y = (-1/9)x +4/9
Find the derivative using limits of
f(x) = 4√(x+2)
f'(x) = (4x)/(√(x2+2))
What is the derivative of f(x) = x3+5+4x3-2x at x=2
f'(x) = 3x2+12x2-2
f'(x) = 3(2)2+12(2)2-2
f'(x) = 12 +48 -2
= 58
What are the three reasons a function is discontinuous?
You can get part $ for this question.
1. A hole
2. A jump
3. Empty sections of the graph.