Can anyone help me out with this one problem please, didn't really learn this type of problem yet. find a and b such that f is differentiable everywhere f(x)= ax^3, x=less than or equal to 2 x^2+b, x=greater than 2 thanks
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You only have problems to differentiate at so you must find such as is continuous and differentiable there, i.e. to find values such as and exists. and so our first condition is . On the other hand, and so our second condition is . Finally and .
thanks for showing me how to do it. just one question, could there be another answer because in my text book it is different than what you gave me.
Originally Posted by soldatik21 Can anyone help me out with this one problem please, didn't really learn this type of problem yet. find a and b such that f is differentiable everywhere f(x)= ax^3, x=less than or equal to 2 x^2+b, x=greater than 2 thanks Continuity at x = 2: a(2)^3 = (2)^2 + b => 8a = 4 + b .... (A) Differentiability at x =2: 3a(2)^2 = 2(2) => 12a = 4 => a = 1/3. Substitute this value of a into equation (A) to get b.
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