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horrorfan [7]
2 years ago
6

Find the values of m and b that make the following function differentiable.

Mathematics
2 answers:
Sonbull [250]2 years ago
7 0
The derivative of f(x) at x=3 is 2x=6 approaching from the left side (apply power rule to y=x^2). The derivative of f(x) at x=3 is m approaching from the right side. In order for the function to be differentiable, the limit of derivative at x=3 must be the same approaching from both sides, so m=6. Then, x^2=mx+b at x=3, plug in m=6, 9=18+b, so b=-9.
Svetlanka [38]2 years ago
6 0

we are given that

f(x) is differentiable at all values of x

so, f(x) will also be continuous at all values of x

f(x) will also be differentiable and continuous at x=3

f(x) is continuous at x=3:

Since, f(x) is continuous at x=3

so, the value of both function must be same at x=3

(3)^2=m*3+b

3m+b=9

f(x) is differntiable at x=3:

Since, f(x) is differentiable at x=3

so, the value of derivative of both function must be same at x=3

f'(x)=2x

f'(x)=m

now, we can set them equal at x=3

2*3=m

m=6

now, we can find b

3*6+b=9

b=-9

so,

m=6

b=-9............Answer

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