Answer to Question #132027 in Calculus for Navya Sharma

Question #132027
Let f(x)={x^2-16x,x<9}{12√x,x>=9}if f continuous at x = 9 ? Determine whether f is  differentiable at x = 9 . If so, find the value of the derivative there.
1
Expert's answer
2020-09-07T19:45:20-0400

The plot of this function is



lower part of the plot corresponds to parabola, upper part - to the square root. This function is not continuous at "x=9" since

"lim_{x \\to 9-0} = 81- 16 \\cdot 9 = -63"

"lim_{x \\to 9+0} = 12 \\cdot 3 = 36"

(this conclusion can be drawn from the plot as well).

The function is not continuous at "x=9" , therefore it is not differentiable at this point.


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