Find a and b if f(x) is continuous everywhere

[@maxamoyal7094]

I LOVE YOU PRIME NEWTONS!! i got a floor functions question on my maths test and knew exactly how to solve it

[@matheuslynus1487]

87😅😅😅

[@teddy6326]

Thank you, Newton, I was really struggling with these types of problems. Big respect ✊🏽

[@safiaatou7]

More Calc 2 content please🥺 You’re the best❤

[@HamzishaMan-r2q]

I appreciate you more live long life I'm from ethiopia 🇪🇹 in oromoo regions

[@LongoliBoniface-z9n]

If I were God I would only add you more years to live forever and ever more, you have really made me understand limits in less than 6 minutes.

[@jacobgoldman5780]

For f(x) to be continuous everywhere, the lim x-->-2 must exist aka lim x-->-2 (ax^2+bx)= lim x-->-2 (ax^3-10b)= (-7x-2)=14. Therefore, a(-2)^2+b(-2)=14=a(-2)^3-10b by plugging in x=-2 or 4a-2b=14 and -8a-10b=14 as well. Dividing the second equation by -2 gives 4a-2b=14 and 4a+5b=-7 and subtracting the second from the first gives (4a-2b)-(4a+5b)=14-(-7)--> -7b=21 or b=-3. Then plugging b=-3 into equation 1 gives 4a-2(-3)=14 or 4a-(-6)=14 or 4a=8 so a=2. Therefore (a,b)=(2,-3) for f(x) to be continuous everywhere.

[@GiftMlinde]

Thenkss sir ❤❤❤❤ U so muchhh, ( 🇲🇼🇲🇼 know as warm heart of Africa)!!

[@teddy6326]

@@GiftMlinde Kenya?

[@fattym193]

Thanks for making understand how to solve this kind of problems newton. You are the best ❤❤

[@MrR9999]

When studying computer graphics many years ago, I recall the importance of C2 continuity for creating smooth curves and surfaces. Perhaps you could extend this problem to a C2 function?

[@bertindiaz1638]

I love your introduction of your videos

[@davidcroft95]

I really like this type of exercise! For fun, I also tried making the first derivative continuous (removing the middle definition, that is redundant), but the solution was the identically zero function 🙃

[@NandiMazibuko-bl5ub]

Keep on doing good work...u make our life

[@gregorysampson9013]

Coolest teacher ever 🎉❤

[@JenniferEze-s8l]

This was really helpful ❤️ thanks alot❤

[@surendrakverma555]

Excellent lecture Sir. Thanks 🙏

[@TranquilSeaOfMath]

Nice example and work through. What type of chalkboard you use?

[@thinz1000]

Thank you, thank you, thank you (south africa)

[@Taric25]

Oh, you made it continuous but not differentiable.

[@Taric25]

@awrRoman25 Yes, I said that.

[@punditgi]

Prime Newtons has it all! 😊

[@ounaogot]

He's the OG

[@mohamedmehdi7478]

The first one that I see this kind of function . Thank you very much. Bye.

[@mychannelforpeople-xw1wl]

You are the best👌

[@WhiteGandalfs]

Why the limes evaluation? Just insert the value at "x = -2" into the two formulars together with the x and solve the simple linear two equations! The derivatives we would need if we would want the crossover to become smooth in the derivatives. But that would require a few more degrees of freedom for our functions.

[@IbrahimMatiko-t2n]

Well explained

[@humnarizwan7834]

thank you so much for the help king! loved it

[@maburwanemokoena7117]

If the question was phrased “Find the values of a and b for which f is differentiable everywhere” we were gonna different values of a and b which satisfy continuity and differentiability.

[@victoriaivatswa9873]

YOU ARE THE BEST

[@LacksonDissi]

Vibrant video

[@DebelaFikadu-fn4wi]

Thanks for ever ❤

[@maxvangulik1988]

a(-2)^2+b(-2)=-7(-2)=a(-2)^3-10b 4a-2b=14; -8a-10b=14 12a+8b=0 a=(-2/3)b (-14/3)b=14 b=-3 a=2

[@maxvangulik1988]

f(x)={2x^2-3x, x-2 f'(x)={4x-3, x-2 although the function is now continuous at x=-2, its derivative isn't.

[@maxvangulik1988]

for f'(x) to be continuous, all we need are different values of a and b. f'(x)={2ax+b, x-2 -4a+b=-7 12a=-7 a=-7/12 b=-14/3 f'(x)={-7x/6-14/3, x-2 f(x)={(-7/12)x^2-(14/3)x, x-2

[@alsa4370]

This man istg saves ass

[@JSSTyger]

b = -3 and a = 2

[@comdo777]

asnwer=2

[@klementhajrullaj1222]

OR, TO SAY IT DIFFERENTLY, WHEN YOU BUILD THE FUNCTION GRAPH, YOUR HAND SHOULD NOT BE INTERRUPTED DURING DRAWING IT!