anonymous
  • anonymous
Let f(x) = 3 x^2 - 8. Find an equation of the line tangent to the graph of f at the point where x = -3. y =
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Mertsj
  • Mertsj
Do you know that the first derivative is the tangent function?
anonymous
  • anonymous
the power rule?
Mertsj
  • Mertsj
Yes

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More answers

anonymous
  • anonymous
f'(X)= rx^r-1
Mertsj
  • Mertsj
f'(x)=6x
anonymous
  • anonymous
that the deriv 6x so plug that in the equation
Mertsj
  • Mertsj
At x = -3, f'(x)=-18 and that is the slope of the tangent at x = -3
anonymous
  • anonymous
y=mx+b right? or y-y1=mx-x1
Mertsj
  • Mertsj
y=6x That is the equation of the tangent function. At x = -3, it has a value of -18 and that is the slope of the tangent at that point.
Mertsj
  • Mertsj
Why don't you draw the graph of the parabola and then draw the tangent at x = -3 and see what it looks like?
Mertsj
  • Mertsj
That would help you understand.
anonymous
  • anonymous
wait what is the full equation y=6x?
Mertsj
  • Mertsj
So if you want the equation of the tangent you know its slope is -18 and you know it goes through the point (-3,19) So use either y= mx+b or point slope form. Whichever you prefer.
Mertsj
  • Mertsj
y=6x is the function that gives you the slope of the tangent at any x value of the parabola.
anonymous
  • anonymous
y=-18(-3)+b
Mertsj
  • Mertsj
\[y-19=-18(x+3)\] \[y=-18x-35\]
Mertsj
  • Mertsj
y=-18(-3)+b 19=-18(-3)+b
anonymous
  • anonymous
for some reason im not writing it corrrectly bcause my book says its wrong
Mertsj
  • Mertsj
what does your book say it is?
anonymous
  • anonymous
equation of the tangent line of y = x3 at x = 2
anonymous
  • anonymous
3 x^2 = f(x)+8
Mertsj
  • Mertsj
We are not working with the function y = x^3. We are doing y = 3x^2-8
Mertsj
  • Mertsj
What does your book say for this one?
anonymous
  • anonymous
it says y=-18x+b
Mertsj
  • Mertsj
For the final answer?
anonymous
  • anonymous
yeah they only want the equation
anonymous
  • anonymous
of a line
Mertsj
  • Mertsj
Well it would be easy to find b and if i were you I would give both answers.
anonymous
  • anonymous
ok thanks
Mertsj
  • Mertsj
Because the problem specifies to find the equation of the tangent at x = -3.
Mertsj
  • Mertsj
yw

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