Use the limit definition of derivative.

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Mika

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Hello...Can someone help me here?
Given the function ?=?^3+3?+1, answer the following items.
a) Find the slope of the tangent line at the point (0,1).
b) Find the equation of the tangent line at the point (0,1). Verify your answer by showing the graph of the function and the tangent line at the given point.
c) Find all points at which the slope of the tangent line to the given function equals 5.

Someone help me...idk about this topic even i study it multiple times. Thank you
 
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Start with finding the derivative of the function. Show us what you've done already.
 
Mika said:
Hello...Can someone help me here?
Given the function ?=?^3+3?+1, answer the following items.
a) Find the slope of the tangent line at the point (0,1).
b) Find the equation of the tangent line at the point (0,1). Verify your answer by showing the graph of the function and the tangent line at the given point.
c) Find all points at which the slope of the tangent line to the given function equals 5.
Click to expand...
If [imath]y=x^3+3x+1[/imath] then the slope is [imath]s(x)=y'(x)[/imath]. So that:
a) [imath]s(0)=y'(0)[/imath]
b) [imath](y-1)=s(0)(x-0)[/imath]
c) [imath]s(x)=3[/imath] solve for [imath]x[/imath].
 
pka said:
If [imath]y=x^3+3x+1[/imath] then the slope is [imath]s(x)=y'(x)[/imath]. So that:
a) [imath]s(0)=y'(0)[/imath]
b) [imath](y-1)=s(0)(x-0)[/imath]
c) [imath]s(x)=3[/imath] solve for [imath]x[/imath].
Click to expand...
can you give me some step to find the slope? thanks
 
Mika said:
Hello...Can someone help me here?
Given the function ?=?^3+3?+1, answer the following items.
a) Find the slope of the tangent line at the point (0,1).
b) Find the equation of the tangent line at the point (0,1). Verify your answer by showing the graph of the function and the tangent line at the given point.
c) Find all points at which the slope of the tangent line to the given function equals 5.
Click to expand...
In your title, you say you need to "Use the limit definition of derivative", but the problem as quoted doesn't say that. If the definition is the only method you have yet to find a derivative, or if somewhere else they made that requirement, then do so; otherwise, use whatever method you know.

What we need to see is where you are stuck in your work, so we can help you there. Show us anything you tried, even if you think it's wrong.
 
Dr.Peterson said:
In your title, you say you need to "Use the limit definition of derivative", but the problem as quoted doesn't say that. If the definition is the only method you have yet to find a derivative, or if somewhere else they made that requirement, then do so; otherwise, use whatever method you know.

What we need to see is where you are stuck in your work, so we can help you there. Show us anything you tried, even if you think it's wrong.
Click to expand...
idk how to start finding the slope
 
Mika said:
d/dx[3x^2 +3]
=3* d/dx[x^2]+d/dx[3]
=3*2x+0
=6x
Click to expand...
It looks like you took the derivative twice. It's just the first derivative [imath]y'=3x^2+3[/imath].
The slope of the tangent line is [imath]y'(0)=3(0)^2+3=3[/imath].
For b), you have the slope from a), and you have a point (0,1) on the line. Can you write an equation for the tangent line?
 
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BigBeachBanana said:
It looks like you took the derivative twice. It's just the first derivative [imath]y'=3x^2+3[/imath].
The slope of the tangent line is [imath]y'(0)=3(0)^2+3=3[/imath].
For b), you have the slope from a), and you have a point (0,1) on the line. Can you write an equation for the tangent line?
Click to expand...
y2-y1=m(x2-x1)
y-1=3(x-0)
y=3x+1
 
BigBeachBanana said:
It looks like you took the derivative twice. It's just the first derivative [imath]y'=3x^2+3[/imath].
The slope of the tangent line is [imath]y'(0)=3(0)^2+3=3[/imath].
For b), you have the slope from a), and you have a point (0,1) on the line. Can you write an equation for the tangent line?
Click to expand...
does this y=3x+1 is the one i need to sketch a graph?
 
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Mika said:
does this y=3x+1 is the one i need to sketch a graph?
Click to expand...
You need to graph both the original function and the tangent line to verify that it is in fact the tangent line at the point (0,1). Are you allowed to use a graphing calculator?
 
Mika said:
View attachment 31471is this the correct step and answer?
Click to expand...
In the first line, you need to use some mathematical notation to distinguish between the original function and its derivative.
3x^2+3 is the derivative, so use f'(x).
Second, why do you have f*3x^2+3=5? What is the purpose of the f*?
However, your answer is correct.
 
ok thanks
BigBeachBanana said:
In the first line, you need to use some mathematical notation to distinguish between the original function and its derivative.
3x^2+3 is the derivative, so use f'(x).
Second, why do you have f*3x^2+3=5? What is the purpose of the f*?
However, your answer is correct.
Click to expand...
 
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