Question

Find the derivative of the function
$f\left(x\right)=2^x+3x-5atx=-1$ at Also show that $f^{{}^{\prime }}\left(0\right)+3f^{{}^{\prime }}(-1)=0$

Answer 1

Consider the given function

$f\left(x\right)=2^x+3x-5=0$

Differentiation this with respect to x and we get,

$f\left(x\right)=2^x+3x-5$

$f^{\prime }\left(x\right)=2^x\log 2+3$

Put $x=0$and we get,

Then,

$f^{\prime }\left(0\right)=2^0\log 0+3=\infty$

Put $x=1$ and we get,

$f^{\prime }(-1)=2^{(-1)}\log (-1)+3=3$

$f^{\prime }(-1)=\infty +3=\infty$

L.H.S.

$f^{\prime }\left(0\right)+3f^{\prime }(-1)$

$=\infty +\infty$

$=\infty$

R.H.S.