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CalculusSuperchallengeThe Derivative

The Derivative · Superchallenge problem

Find constants a,ba,b so that

f(x)={x,0≤x≤4,ax+b,x>4,f(x)=\begin{cases} \sqrt{x}, & 0\le x\le 4,\\[2pt] ax+b, & x>4,\end{cases}

is differentiable at x=4x=4.