Evaluate m to make f(x) differentiable everywhere: f(x)=x^2, if x<=4 and f(x)=m+b, if x>4

DofotheroU

DofotheroU

Answered question

2021-09-15

Evaluate m to make f(x) differentiable everywhere:
K f(x)=x2,ifx4andf(x)=m+b,ifx>4

Answer & Explanation

Nicole Conner

Nicole Conner

Skilled2021-09-16Added 97 answers

For the function to be differentiable everywhere, int has to be contiuous as x=4.
limx4+f(x)=f(4)=limx4f(x)
limx4+(mx+b)=f(4)
4m+b=16i
Check the differentiability as x=4
limx4+f(x)f(4)x4=limx4f(x)f(4)x4
limx4+mx+b16x4=limx4x216x4
limx4+m+1=limx4
m=8
4(8)+b=16
b=16
The final answer:
m=8
b=16

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