The value of displaystylefrac-d-2y-dx-2- the point where f-t-g-t- is0displaystylefrac-1-2-12

Question

Toppr Admin · Accepted Answer

X-f-t-aln-bt-atlnb - -1-y-g-t-b-x2212-ln-at-blna-x2212-t-alnb-x2212-t-a-x2212-tlnb-x2234-y-g-t-aln-b-x2212-t-f-x2212-t- - -2-From equations -1- and -2-xy-1

The value of $\frac{d^{2} y}{d x^{2}}$ at the point where $f (t) = g (t)$ is
$0$
$\frac{1}{2}$
$1$
$2$

$x = f (t) = a^{ln (b^{t})} = a^{t ln b}$ ---------- (1)
$y = g (t) = b^{- ln (a^{t})} = {(b^{ln a})}^{- t} = {(a^{ln b})}^{- t} = a^{- t ln b}$
$∴ y = g (t) = a^{ln (b^{- t})} = f (- t)$ ----------- (2)
From equations (1) and (2),
$x y = 1$

The value of d2ydx2 at the point where f(t)=g(t) is01212

x=f(t)=aln(bt)=atlnb ---------- (1)y=g(t)=b−ln(at)=(blna)−t=(alnb)−t=a−tlnb∴y=g(t)=aln(b−t)=f(−t) ----------- (2)From equations (1) and (2),xy=1

The value of $\frac{d^{2} y}{d x^{2}}$ at the point where $f (t) = g (t)$ is
$0$
$\frac{1}{2}$
$1$
$2$

$x = f (t) = a^{ln (b^{t})} = a^{t ln b}$ ---------- (1)
$y = g (t) = b^{- ln (a^{t})} = {(b^{ln a})}^{- t} = {(a^{ln b})}^{- t} = a^{- t ln b}$
$∴ y = g (t) = a^{ln (b^{- t})} = f (- t)$ ----------- (2)
From equations (1) and (2),
$x y = 1$