Differentiation Question 153
Question: If $ f(x)=\sqrt{x^{2}-10x+25}, $ then the derivative of f(x) on the interval $ [0,7] $ is
Options:
A) 1
B) -1
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
[d] We have, $ f(x)=\sqrt{x^{2}-10x+25}=\sqrt{{{(x-5)}^{2}}}=| x-5 | $
$ = \begin{cases} x-5,x\ge 5 \\ 5-x,x<5 \\ \end{cases} . $ Clearly, f(x) is differentiable at all points on the interval [0, 7] except at x =5.
$ \therefore $ The derivative of f(x) on the interval [0, 7] does not exist.
BETA
