Derek T. answered • 01/27/21
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To find a line that is tangent, you will need the coordinate of the point on the graph and the rate of change at the point.
To find the coordinate plug a=9 into f(x).
f(x)=x2-7
f(9)=92-7
f(9)=74
Coordinate (9,74)
To find the rate of change at a=9, find f'(x) and plug in a=9 into f'(x).
f(x)=x2-7
f'(x)=2x
f'(9)=18
Rate of change= 18
Now you will use slope-intercept form to find your tangent equation.
y=mx+b
rate of change = m
coordinate = (x,y)
y=74
x=9
m=18
74=18(9)+b
74 = 162 +b
b = -88
tangent line equation: y=18x-88
Derek T.
You might have heard of derivatives in Calculus. A derivative, f ‘ (x), is the rate of change at a point. So if you can take the derivative of the original function it turns out to be f’(x)= 2x. I plug in x=9 to get 18 which is the rate of change at x=9.
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02/03/21
Derek T.
I found a few mistakes with my response but it has been fixed!
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02/03/21
Kelvin H.
How did you get 18 when finding the rate of change?02/03/21