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Do you know that the first derivative is the tangent function?
the power rule?
that the deriv 6x so plug that in the equation
At x = -3, f'(x)=-18 and that is the slope of the tangent at x = -3
y=mx+b right? or y-y1=mx-x1
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.
Why don't you draw the graph of the parabola and then draw the tangent at x = -3 and see what it looks like?
That would help you understand.
wait what is the full equation y=6x?
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.
y=6x is the function that gives you the slope of the tangent at any x value of the parabola.
for some reason im not writing it corrrectly bcause my book says its wrong
what does your book say it is?
equation of the tangent line of y = x3 at x = 2
3 x^2 = f(x)+8
We are not working with the function y = x^3. We are doing y = 3x^2-8
What does your book say for this one?
it says y=-18x+b
For the final answer?
yeah they only want the equation
of a line
Well it would be easy to find b and if i were you I would give both answers.
Because the problem specifies to find the equation of the tangent at x = -3.