Question

Let $f\left(x\right)=\{\begin{array}{ccc}3x^2-4\sqrt{x}+1& for& x<1\\ ax+b& for& x\ge 1\end{array}$ if $f\left(x\right)$ is the continuous and differentiable for all numbers in its domain then

• A. $a=b=4$
• B. $a=b=-4$
• C. $a=4$ and $b=-4$
• D. $a=-4$ and $b=4$

Answer 1

The correct option is C $a=4$ and $b=-4$

$f\left(x\right)=3x^2-4\sqrt{x}+1forx<1\&ax+bforx>1Asitiscontinuousf\left(1^{-}\right)=f\left(1^{+}\right)3-4+1=a+ba+b=0As,itisdifferentiable{f}^{\prime }\left(x\right)=\frac{6x-2}{\sqrt{x}}forx<1\&aforx>1so,6-2=a4=ab=-4$
Hence, option 'C' is correct.