Differentiation Question 211

Question: If $ f(x)=mx+c,f(0)=f’(0)=1 $ then $ f(2)= $

Options:

A) 1

B) 2

C) 3

D) - 3

Show Answer

Answer:

Correct Answer: C

Solution:

Here $ f’(x)=m=1 $

Therefore $ f’(0)=m=1 $ and $ f(0)=c=1 $ . Therefore
$ \therefore \frac{dy}{dx}=\frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/2}}[{{\cot }^{3}}x+3x{{\cot }^{2}}x(-cose{c^{2}}x)] $ .