The black curve in the graph below is given by

$y=1\mathrm{.}9e^{-0\mathrm{.}81x}-3\mathrm{.}9e^{-0\mathrm{.}64x}$

a$)$ Find $\frac{dy}{dx}$ and $\frac{d^{2}y}{d{x}^2}$ at $x=1\mathrm{.}3.$ Round your answers to at least $5$ significant figures.

b$)$ Find the linear approximation $L(x)($the equation of the tangent line plotted in dotted blue$)$ to $y$ centred at $x=1\mathrm{.}3($the $x-$coordinate of the red point$).$ Round all coefficients to at least $5$ significant figures.

$L(x)=$

$$

c$)$ Find the quadratic approximation $Q(x)($the equation of the osculating quadratic function plotted in dashed green$)$ to $y$ centred at $x=1\mathrm{.}3.$ Round all coefficients to at least $5$ significant figures.

$Q(x)=$

d$)$ Use the linear approximation from $($b$)$ and the quadratic approximation from $($c$)$ to estimate the $x-$value that gives $y=-0\mathrm{.}78.$ Round your answers to at least $3$ significant figures.

Linear approximation: $x$~~ $$

Quadratic approximation: $x$~~