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Problem 22 Easy Difficulty

If the tangent line to $ y = f(x) $ at $ (4, 3) $ passes through the point $ (0, 2) $, find $ f(4) $ and $ f'(4) $.

Answer

$f(4)=3 ; f(4)=1 / 4$

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Video Transcript

have a question in this. It has given that pendant line to wife will affect passes through the zero common tool. So if this is any curve Well I could have had opinions line And this is for from a three it is passing through 10 comma two. Yeah. Uh huh. We have to find a four and a flash for Okay so let's get started. Well we see that right This four common 3 point lies on this. Why would affect so this is the value of X and this is the value of X corresponds to a value of Y. Our value the function F X corresponds to responding to X equal to full. So we can say that Ben x equal to four. FFS Will be equal to three. So on the other hand on other way we can see that has four equal to three because this is in order to bear for equal to think and we need to find the value of dash for dash police slope of the tangent at this point the flow of attendant at this point will be slow will be the slope of this tendon and the flow of this land which is passing through two points for commentary and zero comma two so half dash four will be able to if this is excellent. This is excellent. Common by one. This is extra. Come away to the struggle. This line will be Y tu minus y one X two minus excellent. So three by two minus three -1 x -4. Given by four. Thank you