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Find the equation of the tangent to the graph of $y=3 x^{2}-x$ at $x=1$

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Chapter 1

Practice Test 1

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so for this problem because we're finding the equation of our tangent line to our graph here. And we can go ahead and start with a stating our knowledge that when we find the derivative, we are finding the slope of the tangent line at one specific point. I'm so essentially are slope of our tangent line. It's just going to be the derivative of this at X is equal to one. I'm so the derivative of three X squared. Using our power rule is will move that to to the front is six x minus The derivative of X is just one I'm so since we know that this is that X is equal to one, we're just going to plug in one for X here and find that are slope is equal to five. And lastly, to figure out the equation of our attention line, we're going to need to find one point on our graph. So the easiest is just going to be plugging in X is equal to one and solving for why so we know that wise equal to three times one squared minus X is one. So this is dressed equal to you too I was. That tells us that we have the 0.12 on our graph. And so using our slope and our point, we can go ahead and find our equation of our tangent line in point slope form, which is why minus whenever the white corner of our point is, which is to is equal to our slope, which is five times x minus the X coordinate over plate. Um and so from here we have the point slope equation of our tangent line to our graph at X is equal to

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