Tangent lines are horizontal

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viathanmk1

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Aug 25, 2015
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So I have two questions one is finding a given slope and the other is finding the horizontal tangent line.

Find the pints on the graph at which the tangent line has slope 11:
y=-.025x^2+7x
Not sure how to get that one. Is there a calculator for this one also to make checking this easier?

Next:

Find the tangent line whose slope is horizontal:
f(x)=6x^2-3x+3
y=-.03x^2-.6x+60

The answers he gave are below but I am not sure how to get the x value so I don't know if they are correct.:
1: (1/4, 21/8)
2: (-10, 63

I used Mathway for those and just plugged in the problem and choose tangent horizontal line to get the y value, but not sure how to get the x value.
 
viathanmk1 said:
So I have two questions one is finding a given slope and the other is finding the horizontal tangent line.

Find the pints on the graph at which the tangent line has slope 11:
y=-.025x^2+7x
Not sure how to get that one. Is there a calculator for this one also to make checking this easier?

Next:

Find the tangent line whose slope is horizontal:
f(x)=6x^2-3x+3
y=-.03x^2-.6x+60

The answers he gave are below but I am not sure how to get the x value so I don't know if they are correct.:
1: (1/4, 21/8)
2: (-10, 63

I used Mathway for those and just plugged in the problem and choose tangent horizontal line to get the y value, but not sure how to get the x value.
Click to expand...

Have you been taught the relationship between:

The slope of the tangent line at a given point on a curve

and

the value of the derivative of the function (describing the curve) at that point?
 
Subhotosh Khan said:
Have you been taught the relationship between:

The slope of the tangent line at a given point on a curve

and

the value of the derivative of the function (describing the curve) at that point?
Click to expand...


So for the first one, take f'(x) and plug in 11 for x?
 
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