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Numerade Educator



Problem 31 Medium Difficulty

Find the acute angles between the curves at their points of intersection. (The angle between two curves is the angle between their tangent lines at the point of intersection.)

$ y = x^2 $ , $ y = x^3 $


$$0^{\circ} \text { at }(0,0),=8.1^{\circ} \text { at }(1,1)$$


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Video Transcript

you have a question and this we need to find there acute angles between two curves at the points of intersection. So let us write down the car's first. Why can't you accept square and why can't two XQ. That point of the section will be by creating access square an X. Q. Okay so access square will be taken as common. The X -1 equal to zero Sex equal to zero and when so if X equal to zero and one. So why will also be equal to zero and one point of intersections will be zero comma zero and one comer. What? No um the acute angle to find acute angle so acute angle between two curves is at any point is the acute angle formed by the attendance at that point. For that. We need to get the slope of the tangent. So let us get the value of anyone by differentiating who I call to access choir with respect to X two X and M2 will be equal to developed by the X in this case three X square. So everyone at zero is 0 and M two at zero is zero and one at x equal to one is 2 and AM two XX equal to one is 3. So acute angle we know that tan theta is am one minus M two by one place and want him to mud 10 30 will be M one to minus three By 1-plus 6 model S So 10 Theta will be -1 x seven modelers which means Then think I will be equal to plus -1 by seven. Yeah so angles will be data either then in verse one by seven which will be able to turn in verse one by mm eight point well three degrees or theater too. Getting worse -1 x seven. The universe mine is run by So this is -8 13 degrees -8.130 DB. Well, this could be done is Uh one of the 80 minus. Okay, so this is going to be obtuse angle, So acute angle is 8.13°. Thank you.