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Problem 49 Medium Difficulty

Given that the graph of $ f $ passes through the point $ (2, 5) $ and that the slope of its tangent line at $ (x, f(x)) $ is $ 3 - 4x $, find $ f(1) $.

Answer

$$
f(1)=8
$$

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Video Transcript

all right. Excuse me. We've got a question here. They give. We're told that given the graph that passed through the 0.25 that slope of the tangent line at X ffx is three minus or of X, and we wanna find F one. Alright, so here we want to we know that the slope of the line is the ratio between why and the X coordinate. So we could say that our slope over the tangent Linus three minus four x. You could say that he first route. Excuse me. The first root of X first derivative of the function of X is the slope, which is three minus x. And then if we took the integral of X, we could calculate we took the integral of the first of X. We calculate the ffx, which would be minus four folks. He looks, which comes out to three. X one is two x word. Awesome. Okay. We know that the line passes through 0.25 That means that when X is to function of X is equal to five. So I would say we have five here. We have three to minus. This is the function of X, by the way. So you have three times two minus 22 squared plus c. So we take five minus six plus eight equals to see. Sees equal to negative seven, actually. Positive. Seven. Sorry. Not a negative. Uh huh. Company. Go ahead and tweet that out there. All right. Now, if we write out our function of X, Yeah, it's a function of X is the same thing as three X minus two X squared Question. Now, if we wanted to calculate the function of X one, that's just one we would do three times for one Linus to one squared plus seven, which is equal to three. Minus two plus seven, which is eight. Right. And that will be our final answer there. I hope that clarifies the question. Thank you so much. Watch

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